John Stewart wrote:

Ian Iveson wrote:

"John Stewart" wrote

...
In your example the DF for the group is 50. However, for each
speaker the source
impedance would be the amp Ro of 0.5 ohms plus the entire series
complex impedance's of
the other nine speakers in the group. That is a condition I would
prefer to avoid.
...

Seems to me this is the crucial point, John. Could be seen as
another example of current sources in series.

cheers, Ian

Nature (And Physics) abhor certain conditions. One of them is current
sources in series. By way of 'The Principle of Duality' another would
be voltage sources in parallel. The definition of each should tell us
something. A perfect current source would deliver the same current to
the load no matter what the load was from a short circuit & on up.
Similarly, a voltage source would deliver a constant voltage to the
load from open circuit & on up to ever increasing currents.

Fortunately for us, most of the circuits we have to deal with include
some positive resistance in parallel with a current source & a positive
resistance in series with a voltage source. That helps us quite a lot
to establish an operating point. Without those resistors the circuit Q
point becomes indeterminate. So a simple current source while not
perfect would be able to source a reasonably constant current over a
wide range of loads. The max load is simply limited by the max voltage
available.

If a negative resistance were to be introduced into the circuit than we
have the potential for an oscillator.

So, I would sure agree with your point Ian, in particular at the
resonance F of the speakers.
Z tends to get quite high at that (those if a bass reflex) point. Even
at mid-frequencies far from the speaker resonance, nine speakers would
add up to 45 ohms. The source for each speaker if all were simply
series connected as Patrick T remarked in the first paragraph of his
original post of April 27th would than be 45.2 ohms. For each
individual speaker, particularly at resonance the remaining speakers
form a rather good current source. If Patrick didn't mean them to be
all wired in series he should have made that clear in his post. The
second paragraph of his original post has the speakers all in parallel.
What next?

I see in Patrick's later response to my critic of his post that he has
suddenly got the clue to series/parallel the speaker array. I wonder
where he got that idea!

You have quoted me out of context and you alleges that I got the idea of
series and parallel combos of speakers from you.

Not so; known about all this for years before ever hearing what you had to
say.

But where you have say 4 speakers in series and each is 45 ohms at Fo,
then then one could say each one sees a drive impedance of the Ro of the
amp
in series with 135 ohms, and the DF is indeed very crook.

But it isn't, its very good.

Where the impedance of all the series speakers is the same, there is
an equal division of power in each one, and at all F,
and the response from each will be the same for the lot.
There is no manifestation of a speaker seeming to be driven by an impedance

of 4 times its own, just because you have series speakers.
This was the point I have been trying to make.

I have series speakers in a Dapollito arrangement, and there
is no DF problem.




As always with anything, including technical advice, Caveat Emptor.

More to go on this yet. And,
Cheers John Stewart

PS- I guess I will have to post the graph showing individual (2,3,4..)
harmonics for pentodes. It is not it in RDH4, but it does show up
elsewhere. That way one can see why a steeper load line is a better
condition for pentodes, again opposite Patrick's opinion.

One could have a very low RL, akin to a short circuit, say 500 ohms for
an EL34.
The distortion will be an unhappy picture.

IN fact the distortion with low loads becomes dominated purely
by the gm variation at varying Ia, and boy, do most pentodes vary!
Triodes have varying gm with Ia.

Triodes are virtual pentodes with a shirtload of internal NFB,
so that with no Ia change there is maximum NFB applied electrostatically,
hence they are very linear with no current change, as when loaded with a
ccs.

Pentodes on the other hand are attrociously non linear when no
NFB is applied internally because the screen stops it.
Gain when loaded by a CCS is extremenly high, about 130 for EL34,
and maybe 3,000 for a 6AU6.
Fortunately, the huge gain gives us an ability to apply
NFBV in external loops.
But still you end up with the same spectra of thd products plus a few
extras
from imd, although at low levels. Still not as clean as triodes.
But with either a too low load, or a too high load, pentodes
and beam tetrodes are disgusting.



Best example
without having to look it up would be the steeper loadline applied to
PP amps. That helps to reduce the 3rd harmonic & one of the reasons we
do it.

Next time you measure a class AB pentode amp
try reducing the RL to 1/4 of the load needed for maximum pure class A.
Then you find the amp works in class AB, and the 3H is far greater at all
power levels.

Beam tetrodes fare better than pentodes, if that makes you feel any better.

6550 can be configured to make under 1% thd
at 40 watts in pure beam class A.
Reducing RL isn't going to reduce the thd.



Depending on speaker resonance & program material, the tube is
always well loaded, both above & below the knee. Below the knee at
speaker resonance & above the knee at
mid-frequencies. JLS

But music has multiple frequencies, During bass notes where the
speaker Z = 40 ohms, the pentodes are loaded with a class A load, large v
swing,
low current swing.
But *simultaneously*, at some other F, say 300Hz, the tubes are loaded by a
Z at say a crossover F
between bass and mids where Z = 3 ohms.
What sort of load line appears then?

Speaker load lines are dynamically variable, so a
an elipse coloured grey for its whole enclosed area is a better idea of a
speaker load.
Resistances offer the only black line load.

And in class AB amps the load line changes from 1/2 RLa-a to 1/4 RLa-a
during each cycle which involves transition from A to AB.

So with a fixed R load value at the output, the load seen by each of a pair
in PP
is a bent line, or a curved one.

The changes in pentode gain between A and AB causes a lot of odd order thd.

PP triodes exhibit the gentlest transition from A to AB, so they
have the least odd order generation due to crossover,
offset by the way gm increases with Ia, so as load
drops with class AB, the gm increases, and so does gain......

Patrick Turner.