Re: RL in Class A SE, an alternative view was Re: Class-A RL determination in SE amps.



Andre Jute wrote:

I'm making a subthread for this because I don't want that muscular
brickie Patrick Turner to come beat the *** out of me for going off on
a completely opposite track and thereby wrecking the possibility of
good discussion of his main points. Patrick is answering the question
"What determines output power of a tube?" as if it were" What
determines maximum output power of a tube?", which is a question that
gives away someone's status as an "engineer" or a newbie, whereas my
argument assumes the question is "What determines desirable output
power of a tube", which is the question asked by experienced
audiophiles who already know that the speaker determines everything.
The two outlooks may appear on the surface to have the same math but
they aren't really interchangeable, or at least they require a lot of
courtesy to rub together amicably, hence the need for a separate thread
so as not to cause confusion. Nonetheless, I've tried to relate the two
outlooks because anyone who has more than one or two amps probably has
at least one amp built to each outlook, or is thinking he might next
try an amp built to the other outlook. (Check out the lively recent
threads on cheap Chinese amps.)

Don't worry Andre, I ain't in the habit of putting obstreperous authors into
the big
mortar mixing machine with a few bricks to sort them out.....

My fundemental formula, RL = Ea / Ia - 2Ra will hold true for ALL loadings you
may wish to use
for most triodes.
For example, for a 300B you could use Ea = 400V and Ia = 60mA, so the tube Pda
= 24 watts only, and get
RL = 6,666 - 1,600 = 5,066 ohms. Max class A power = 6.3 watts and any load
each side of 5k will produce less po.

Where you have very sensitve speakers or horns, there is OODLES of power;
clipping won't happen,
and the relaxed Pda = 24 watts will do fine and the tube will last and last.

The load value tolerance for SET isn't too bad in fact, and speaker Z can vary
to reflect an anode load
between 2.5k and 10k without much of a problem if the power levels wanted are
low.

I myself recommend that a speakers lowest impedance be matched to the anode
load at which max class A power is developed, so that if you have an 8 ohm
speaker which has a typical dip in Z to 5 ohms, then
the OPT will have 1,000:1 Z ratio so that when the speaker is at 5 ohms, the
load is 5k.
At 8 ohms, the anode will see 8k, but although the power will maybe be only 4
watts before asymetrical clipping
occurs on one side of the wave, the distortion will be 1/2 that occuring where
RL = 5k.
And the damping factor will rise to 10 when RL = 8k instead of 5k.

Considering my original post you are replying to, if you STARTED with the 400V
x 80mA idle condition, Pda = 32 watts, then a lot more output power is
available, and the load can be as I calculated at 3.4k, so a speaker could
have a dip to 3.4 ohms without worry with a 1,000 :1 ZR.
Using 8 ohms at the sec the anode load is 8k, and because the Ia is higher,
there will slightly less
load swing into 8k compared with the lower Ia condition.
So output power will be less with the higher load and higher Ia.
BUT, the distortion around the working point for 32 watts should be lower than
when Ia is lower.

In other words, with greater Pda, and providing Pda is well within ratings,
distortion and percieved
sound quality should improve slightly with higher Ia than lower Ia for the
first all important watt or two.

And going back to my application of the reasoning to a 12AX7, one can use
a 220k anode dc supply resistor if you want, its about 3 x Ra, but
using a CCS dc supply is better, so the tube only sees the following cap
coupled bias R of say 470k
as its load.
The distortion, which is miniscule with 12AX7 at a few vrms output will be
halved,
and the sound should ascend to that created by angels.

My simple fomulaic method of Load Value Establishment for SE amps
can be a starting point for many, and after grasping the fundementals they can
tweak at the edges.

Patrick Turner.









********
Patrick Turner wrote:
There is a simple way of determining the load and power for an SET tube
amp
without drawing graphs or doing much calculation.

If you're slack enough to grasp at that straw, better not work with
expensive tubes until you have much more experience. Remarks by Patrick
further down about novices who won't do the work apply doubly.

The point about working graphically on the curves is that all
considerations are visible, and in a form that breeds understanding of
tube operation. What Patrick is suggesting here is a form of mental
arithmetic best done with the transfer curves in front of your, at
least until you have committed them to memory (it happens naturally if
you specialize in one or a very few tubes, as I do).

Let us suppose we wish to find out what is the RL for which maximum
class A power can be developed
for any suitable quiescent operating point for a triode.

Bad way to start, given that this is a Class A SE amp, which comes (or
should come, in my mind anyway) with the assumption that we are willing
to trade power for a very, very quiet sound.

A better way to start, though it takes restraint and a breadth of
atitude newbies find hard to maintain, is to ask, What is the minimum
power I require with my speakers, then to choose a tube with several
times that power in triode operation, then to flatten the nasty higher
and odd harmonics with an extraordinarily high load on the power tube
i.e. a high primary impedance on the output transformer, which will
have a flattish slope. You're now sacrificing power for low harmonics.

We look at the data and makers curve sheets.

We see Ra, the plate resistance.

We see what the max Pda is for the triode.

We locate a quiescent operating point so that Ea x Ia = 0.8 x max rated
Pda.

We choose a quiescent anode voltage, Ea.

Ia = Pda wkg / Ea.

RL for max class A for this Pda and Ea = Ea / Iaq - ( 2 x Ra ).

Max power output = Iaq x Iaq x RL/2, where Iaq is the idle current,
and which also is the peak value of the load current swing.

This all ignores the mainly 2H distortion, but if NFB is used, the
formulas here
will work, becauswe the NFB will force the anode current swing to be +/-
Iaq peak.

In my alternative version, where the output power will be lower
*because it is limited by my assumption that noise rather than power is
he most important design parameter*, no NFB or very low NFB will be
required. NFB isn't a direct substitute to my low-noise paradigm
because it moves the distortion spectrum into the higher and odd
harmonics which are especially troubling to the human ear.

This isn't a minor difference of emphasis: this is the key difference
between Patrick's entirely reasonable mainstream approach and my
"ultrafidelista" approach.

So take a 300B with Pda = 40 watts.

Pda working = 0.8 x 40 = 32 watts.

Suppose we wish to use Ea = 400V, then Ia = 32 / 400 = 0.08 amps.

RL = Ea/Iaq - 2Ra .

Ra = 800 ohms from the data,

So RL = 400/0.08 - ( 2 x 800 ) = 5,000 - 1,600 = 3,400 ohms.

Max PO = 0.08 x 0.08 x 3,400 / 2 = 10.8 watts.

This amp will, surprisingly in the light of what I said above, actually
sound good if the speakers are reasonably sensitive and the amp
therefore works on the linear part of the transfer curve, before the
3K4 loadline comes too close to the part of the graph where the
loadline approaches the curvy bits at the bottom of the negative bias
lines. See what I mean about the graph teaching a lot about tube
operation that you already have to know (and know well) with Patrick's
mathematical version?

Without NFB the 2H thd will limit the Vswing about 10%, so with less
swing without NFB,
unclipped po = 0.8 x 10.8 = 8.7 watts, ( because power output is
prortional to VRL squared,
so with 90% of the theoretical v swing, po will be 0.9 x 0.9 theoretical
po...)
So with OPT losses we end up with about 8 watts.

A 300B is an expensive tube. This rough and ready mathematical method
assumes you'll be running the 300B at 400V (actually 396V with gennie
modern production WE300B -- see the curves on my netsite) on the plate
and 80mA. With autobias and the copper loss in the transformer primary,
your B+ after the power filter must thus be just short of 500V. Even a
5 per cent variation in the mains and suddenly you're running your
expensive tube at 84mA, which isn't a longlife option, and doesn't
leave scope for further line variation.

The same formula can be applied to pentodes and beam tubes but the Ra
data figure
for pentodes must never be considered.

People with Sofia curve tracers have put accurate data for common
pentodes, and perhaps others I have not looked for, on the net. The
triode curves for EL34 on the net I know from experience to be spot on.

( I make no apology for the way the God Of Triodes designed the
universe;
pentodes and beam tubes and indeed some high mu power triodes
need to be to be considered with exceptions to simple triode rules in
mind, and exceptions were
deliberately included to confuse the begginner who struggles to
understand
the most basic fundementals of device behaviour. Beginners who refuse to
learn to take in basics and
exceptions and complex concepts will be rewarded with clouds of smoke
shortly after turn on.... )

Make friends with your local elderly ham radio operator. Read RAT.
Don't be afraid to ask stupid questions; the guys who sneer at your
ignorance are performing the useful service to you of marking out any
advice they do give you as doubtful. The guys who made radar work in
their old age corresponded patiently with me, a crash course in
electronics you can't pay for at any university.

The line on the beam&pentode anode curve graphs which determine class A
load swings
is that which is steep, and on the far left of such graphs, and to the
left of the knee
of the plate resistance curves for the various values of grid voltages.
This line governing the extent of the negative going Vswing limit,
Ea-min, is usually one for most octal power tubes
which has a slope for where there is 400mA of Ia change for 100V rise in
Ea above 0V.
So for most beam&pentodes, Ra' = 100/0.4 = 250 ohms.

So for many beam&pentodes, the RL for most class A = Ea / Iaq - 500.

So consider a 6CA7 Pda max = 28 watts, so wkg Pda = 22.4 watts.
Select a suitable Ea between 250V and 450V, say 350V,
then Iaq = 64mA.

RL = 350 / 0.064 - 250 = 5, 218 ohms.

Or better still 5K6, so that when you break up this amp to build that
300B in your dreams, you don't have to buy new transformers. I'm a big
fan of the LL1623 90mA SE output transformers from Lundahl which have
excellent connection facilities for various output impedances,
including 5K6.

Maximum PO = 0.064 x 0.064 x 5218 / 2 = 10.69 watts.

Without NFB, Distortion will limit po to around 8.6 watts,
and OPT may claim some power loss so expect 8 watts total.

The zero loop NFB 300B efficiency is 8/40 x 100 = 20%.
The zero loop NFB 6CA7 efficiency is 8/22.4 x 100 = 35.7%.

The 300B will sound many dB better than the 6CA7.

However, if you follow the highly sensitive speaker, low odd harmonics
paradigm to its logical conclusion and make your 6CA7 into a
triode-linked Class A SE amp, you can still get around 2W of glorious
sound and those of us who live in 220-230V mains regimes can do it on
the cheap with standard isolation power transformer and 380V caps often
on sale through catalogues.

This could give you sound quality only a few dB less than 300B, for
many, many dB less money. If you forget about the street cred of the
fashionable SE, you can build a Class A PP ZNFB triode-linked EL34 for
less money that will come to very, very near a 300B, and if you build
it expensively (damned nearly the price of a reasonable 300B amp) will
match the 300B all the way and have 3dB to spare in case you want to
divorce your first choice of speaker and replace it with a younger,
less sensitive model.

See, it is all about the speaker choice you make, very little to do
with amps. The speakers determine the power you require, which in turn
determines the tube you can use, which in turn determines how expensive
it will be to trade in available power for silence.

Costs are often deceptive. For practical purposes, all really good
Class A tube amps cost about the same (more than you want to admit if
you're socially sensitive) and sound about the same (exceptionally
involving). Good speakers can be relatively cheap -- if you DIY! Really
good speakers bought in a shop will always cost several multiples of
even a really good tube amp that you built yourself.

The use of a single power bjt or mosfet to achieve the same class A SE
watts
will give class A efficiencies of about 40% and 45% respectively,
but the harmonic outcome of either SS device will be like the 6CA7and
not very nice,
and buckets of loop NFB NEED to be used.
The 200B already will have internal NFB applied, and its
damping factor with a 3.4k RL is around 4.

The Ra of the 6CA7, the dynamic Ra is about 15k, or about 5 times the
load
of 5.2k so the DF is a lousy 0.34.

Still on the assumption that we are writing for aspirants -- a bit of a
stretch, eh Patrick? -- this is symptomatic of the 101 things a tube
amp designer has to keep in mind. If you're a novice, don't sweat it.
Make your design, or choose your design, and come on RAT and we will
tell you the complicated details one by one. If you keep a humble
attitude, no one will eat your lunch.

The bjt or mosfet also have a drain or collector output resistance of
many times the load value
and have natural DF worse than the beam or pentode tube.

The use of the load value for SET being that which gives the maximum
class A for the amount
of dissipation chosen isn't always waht we may want for best fidelity.
So a load of 7k for the same Iaq and Ea as in the above example will
give a DF=8,
and maybe less than 1/2 the thd with RL = 3.4k.
The po will not be Iaq squared x RL/2.

Aha! I see Patrick is there but I will let my remarks above stand.

But with a higher value load, the Ea mimimum swing will be less than
Emaximum possible;
the Emin is limited by the Ra line where Eg = 0V, and to find the swing
we need
to be better at math or be able to cope with a graphical solution.

The problem with this, Patrick, is that everyone here has done this for
so long, we do the mental arithmetic and can't remember that we once
pored over the curves and tried to make finer measurements than they
really support. I repeat, in my opinion the graphical solution is
actually the easiest one.

Similarly, with a load lower than that which is for maximum po, the
Eamax is limited by
current cut off in the tube, and in this case for all values of RL lower
than
that giving max po, and equal +/- Ea swings, po will still be equal to
Iaq squared x RL/2.

The formula I have nominated for RL values for triodes
will work for a 12AX7 with Ra = 65k, Ea = 200V, Ia = 0.6mA.

RL = 200/0.0006 - 130,000 = 203,333 ohms.
Hence we so often see 12AX7 loaded with 220k and cap coupled with a 1M
following
grid bias R.
Pda of the 12AX7 selected here is way below the limits for the tube, so
we don't need to
worry about Pda for the equations.

If you farnarkle around with a set of tube curves and you are good at
drawing triangles
you will see what I say gels.

No doubt about it.

But if you marry sensitive speakers first, you can get superior sound.
As a next step, choose a primary impedance of 6-8x the plate
resistance, lay it on the transfer curve at as high a current and plate
voltage as you can afford (tube longevity) and restrict the signal so
that it never comes anywhere near touching distance of the 0V bias line
(you won't need to worry at the other end of the signal swing because a
flat impedance, high current topology will never dip into the nasty
illinearities which lurk there), and you will have wonderful sound.


Patrick Turner.

Isn't it wonderful to have choice?

Andre Jute
Visit Jute on Amps at http://members.lycos.co.uk/fiultra/
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for the tube audio constructor"
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