LOAD MATCHING 4.
BEAM TETRODE  PUSH PULL AMPLIFIERS.
Last edited 2012.
This page is about.....

Beam tetrode background.
DESIGN METHOD, PP CLASS AB1, BEAM TETRODES. 
Fig 1. Loadline graph drawn on anode curves for one 6550 of a PP pair with
4k0 a-a load.
Steps (1) to (10) for working out load, AB1 power for a pair of 6550, KT88.
Plotting loadlines for EH6550 tetrodes, 
More relevant notes about design concerns.
Fig 2. Graph for power output versus anode and speaker load.
Notes about 56W with class AB1 and 28W for class A and speaker sensitivity.
DESIGN METHOD, PP CLASS A1, BEAM TETRODES.
Fig 3. Loadline graph drawn on anode curves for one 6550 of a PP pair with
8k0 a-a load.

Biasing the output tubes,
Distortion,
Output resistance.
Using a higher RL such as 8ka-a,
Global NFB, its effect on output resistance,
Calculation of amount of applied NFB and the output resistance with applied NFB.
Fig 2. Graph  of power out vs RL .
Loading the PP beam tetrode output stage, OPT ratios.
Ultralinear and other output tube configurations,
Driver amplifier comments.
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Beam Tetrode background.
Many people firmly believe that beam power tetrodes offer excellent hi-fi sound
quality. The most famous beam tetrodes are the 6L6, 6V6, KT66, 6550 and KT88.
We now have the Russian made KT90EH, and recently the KT120EH.
Before beam tetrodes were invented, a Mr Telegen working for Philips invented the
pentode in 1926 at the Philips research labs.
Anyone wanting to make a pentode
other than Philips had to pay royalties to Philips who owned the patent. To avoid
the patents issue, beam tetrodes were invented in the early 1930s by the MOV

(Marconi-Osram Valve, a subsidiary of EMI jointly owned with General Electric
Company plc
) and marketed this tube family under the sobriquet "KT", meaning
"kinkless tetrode".

Because MOV's engineers did not feel the kinkless tetrode could be successfully
mass-produced, they licensed the design to RCA. This proved to be a poor business
decision on MOV's part. RCA subsequently had enormous success with the 6L6.
It replaced the use of power triodes in most public-address amplifiers almost overnight.
So many applications were found for the 6L6 that a complete list would be impossible
to assemble. MOV introduced their version, the KT66, a year later.
Today, there are a considerable variety of power output beam tetrodes and pentodes
being made such as 6V6, 807, 6L6, 5881, KT66, 6550, KT88, KT90, KT120 beam
tetrodes and EL84, EL34 pentodes.
There are those who might argue which sound best, or whether real triodes such
as 45, 2A3, 300B better still. But I think just how such tubes are used will
determine the sound to greater extent.

Not many hi-fi fanatics complained when pentodes and beam tetrodes were
invented because hi-fi sound from recordings on disc or tape was a thing of
the future in 1933. But arguments about which sounds better, multigrids or
triodes have been going on now for at least 75 years among audiophiles who
have had access to hi-fidelity source material since the 1950s.

The beam tetrodes and pentodes have a screen grid which prevents the
internal NFB of a triode having much effect to keep Ra low and THD low.
Without the triode's NFB, tetrode and pentode anode resistance, Ra, is much
higher than the anode load and there is much more harmonic distortion than
any "nice" triode like the 300B. So unless external loops of NFB are used with
multigrid tubes, and to reduce Ra and THD to similar levels found in a triode,
the multigrid is always likely to sound worse than the triode.
The 300B began production in 1928, and worked fine without any loop NFB.
Harold Black invented NFB, ( Negative Feed Back ), in 1928.
NFB added circuit complexity in 1930 and it wasn't easy for technical staff to
understand it because it required wide bandwidth output transformers and a
good working knowledge of practical ways to avoid amplifiers from becoming
unstable and oscillating when FB networks were connected.

But tetrodes and pentodes were twice as efficient as triodes, and a loop of
NFB was cheap. The tetrode / pentode voltage gain was high, so they were
easy to drive. If a NFB loop is added to an amp, the overall gain is reduced
by the NFB. If the reduction of tetrode gain with external loop NFB becomes
about equal to triode gain, then the tetrode amp used the same number of tubes
as the triode amp, and had similar THD and output resistance as the triode amp
without any loop NFB. Just about all tetrodes and pentodes may be "triode connected"
with the screens tied to the anode, and a 6550 or KT88 may be made to give similar
"triode strapped" performance as a 300B which has about the same anode dissipation
rating as 6550 or KT88.
But the tetrodes could produce twice the power of triodes. Hence the 6L6 was a
huge success, along with EL34. The 6CA7 was invented to be a US made plug in
replacement for the European made EL34. The KT88 and 6550 entered the scene
in the late 1950s and gave a huge boost to performance possible from 2 tubes, as
the single KT88 or 6550 could do the job of two 6L6.

The 6L6 had a cousin, the 807, meant for RF amplifiers and the 807 helped win WW2
for the allies. Millions of 6V6 were  used in countless AM radios as the 3 watt audio
output amplifier.
The sound from AM radio with a 6V6 was quite awful when you turned up the volume.
But loudspeakers were very sensitive. Many radios did not include any loop of NFB.
People did not complain much because  the source signal was often lousy
anyway. The sound of a 78 rpm shellac record transmitted on AM with 3 kHz audio
bandwidth and with 5% THD was a cause to get drunk.
Certainly if Marlena Dietrich was singing.

So here we are in 2011 with triodes, pentodes and beam tetrodes. Marlena went North,
and the sound sources have vastly improved, and the vast majority of people use
transistor amps with a huge amount of loop NFB. Some audiophiles have grudgingly
accepted that you could connect the tetrode or pentode screen grid to the anode and
have a nice triode if you really had to have a triode. A 300B is quite expensive for
what it is and what it does, and should be cheaper than KT88 or 6550 because less
parts are inside. 
My pages on load matching to SE and PP triodes illustrates what can be achieved
with the 6550, KT88 or KT90 in triode compared to a 300B.

There are several ways to linearize beam tetrodes and all involve NFB. I prefer
using a cathode feedback winding which is a 10% to 20% portion of the total primary
turns on an output transformer so that the tetrode or pentode ends up having overall
voltage gain of about the same as a 300B, ie, less than 4.0, but while preserving the
ability to make twice the power of triode power and be easily driven without grid
current.
The amount of FB is thus about 8dB to12dB of applied local NFB in the output stage.
In Quad-II amplifiers this method was patented and it is officially called the
"Acoustical Connection." This CFB method is the best known simple application
of the idea with 10% of the primary turns in the form of a tertiary winding with
centre tap which is about 8 dB of NFB. This makes the KT66 used in Quad-II
amps behave almost identically to the same tube strapped as a triode but the power
output is double that of using KT66 connected as triodes.

For hi-fi amps the "Ultra-Linear" connection has been the most popular since 1954
because instead of a tertiary CFB winding the UL connection requires only two taps
on the anode primary winding to send between 25% and 70% of the anode signal to
the screens which converts tetrode operation to an intermediate operation between
pure beam tetrode and triode. Such a method allows nearly full power of the tetrode
but with triode's lower distortion characteristics. Ra can be reduced usefully from
say 30k ohms to 5kohms or less, depending on the UL tap percentage.
McIntosh went further than Quad with CFB where the OPT tertiary CFB winding
had the same turns as the anode primary winding. The amount of CFB was 50%
which is about 16dB of applied NFB and 50 Watts could be safely had from a
pair of 6L6 in class AB beam tetrode way back in 1949, and with measurements
better than everyone else since there was also 20dB of global NFB applied.
Some would argue the McIntosh was a class B amp with lots of NFB and it
could not sound as well as the same tubes working in class A UL with normal loop
NFB. I'd rather have 2 x KT88 / 6550 to get 50 Watts in class AB1 than having 6L6
with low bias levels and working slightly into class AB2.

Nothing prevents the use of the beam tetrode connection with only global NFB if you
have a good OPT and there is at least 20dB of global NFB. The benefits of the UL
or Acoustic method is that most of the distortion is reduced in the output stage
and less global NFB may be used, and stabilization of the amp is easier.

Most guitar amp makers never use much NFB and nearly always use ordinary beam
tetrode or pentode connection because both musicians and public like the distortions
of pure PP beam tetrodes or pentodes. This seems so true when you realize every
musician does not like to use a transistor amp and must have a tube amp.
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DESIGN METHOD, PP CLASS AB1, BEAM TETRODES.
Fig 1.
Graph of GE6550A
        tetrode loadlines for PP.
Fig 1 shows anode data Ea vs Ia curves for Ra of the 6550 beam tetrode.
The drawn load lines are explained below for class AB1 PP operation of
two 6550.


Notice that the there is a limit to how low the Ea voltage may swing.
Ea swing is not possible to the left of the "limiting Ra line" or by what is also
known as the "diode line" shown above between 0.0 and up through F and B.
The ohm value of this limiting Ra line may be calculated as approximately
Ea / Ia for point B, which is at the knee of the Ra curve for Eg1 = 0V
when Eg2 = +250V. The Ea and Ia at point B are 56V and 340mA,
so the Ra limiting line = 65 / 0.34 = 191 ohms.

The Eg1 bias voltage = -20V below the cathode Ek for 6550 with CFB use
or pure beam tetrode where Eg2 is a fixed 250V above the Ek, for Ia idle
= 80mA. Where UL or triode connection is used with Eg2 = Ea = 400V,
then the Eg1 grid bias voltage must be increased to approximately -35V.

When UL taps or CFB windings are used the slope of the limiting line
leans over more towards the right, ie, the ohm value is higher at approximately
280 ohms for many tube types. Where the curves are unknown, it is often
OK to assume the Ra limiting line = 280 ohms.

(1) Choose operating conditions at idle for each 6550.

Pda = 32 Watts. Ea = 400V. Ia = Pda / Ea = 32 / 400 = 80mAdc in each 6550.


For Hi-Fi amps, the maximum Ea values for various beam tetrodes
and pentodes are listed here :-
+520Vdc for 6550, KT88, KT90,
+430Vdc for KT66, 6L6GC, 807, 5881, EL34,
+330Vdc for 6V6, EL84.


Pda per tube in class AB HI-FI amps at idle should NEVER exceed
0.75 x rated Pda maximum given in tube data specs. Pda at idle seldom
ever needs to be more than 0.6 x Pda rating.

(2) Calculate absolute minimum RLa-a.

Examine tube data sheets and see knee of Ra curve for Eg1 = 0V.

This is point B in above Fig 1.

Point B on Ra curve must not be above the curve line for Pda = 42 Watts.
If so, Point B may be where Pda max of 42 Watts intersects Ra curve below
the knee.
Read off the Ea and Ia for point B.
Ea = 65V, Ia = 340mA.

Point B gives the Ea minimum and Ia maximum for the minimum class AB
load for one tube, RLa.

Calculate the theoretical minimum class B load for one 6550.
Class B RLa = ( Ea - Ea minimum ) / Ia maximum.

= ( 400V - 65V ) / 0.34A = 985 ohms.

Anode to anode load, RLa-a = 4 x Class B load.

= 4 x 985 =  3,940 ohms; round up to 4,000 ohms.

RLa-a = 4,000 ohms,
RLa = 1,000 ohms.

(3) Calculate Ia change for RLa from 0V to Ea at idle.
Ea at idle = 400V.
Ia change 0V to 400V = 400V / 1,000 ohms = 400mA.

(4) Plot point A on Ia axis for 400mA calculated in (3)
Draw load line for 1,000 ohms from point A to point D on Ea axis where
Ea = 400V.

(5) Point B on Ra curve for Eg1 = 0V where RLa 
load line
intersects Ra curve.

RLa load line for 1k0 intersects Ra curve at point B where Ia = 340mA
and Ea = +60V.
The Ea = +60V is the Ea minimum.

(6) Calculate Ea peak voltage swing and PO into RL a-a.
Ea peak voltage swing = Ea - Ea minimum = 400V - 60V = 340Vpk.

Class AB1 Power = 2 x (Ea - Ea min) squared / RLa-a.

Class AB1 Power = 2 x 340 x 340 / 4,000 = 57.8 Watts

(7) Calculate class A1 power portion of total AB1 power.
Class A1 power for both tubes = 0.5 x Iadc squared x RL a-a,
where Iadc is for one tube,
= 0.5 x 0.08 x 0.08 x 4,000 = 12.8 Watts.

(8) Calculate class A load for each 6550 and draw
class A load line.

Class A RLa = RLa-a / 2 = 4,000 / 2 = 2,000 ohms.
Calculate Ia change for 0V to Ea change
= Ea / class A RL = 400V / 2,000 ohms = 200mA.
Add Idla Ia dc at Q to last result, 200 + 80 = 280mA.
Plot point E on Ia axis where Ia = 280mA.
Draw straight line from E through Q and to intersect Ea axis at point G.
Plot point C where the two loadlines E-G and A-D intersect.
Draw vertical line from point C to Ea axis and read Ea voltage.
Ea = 240V. This voltage is the Ea minimum for the maximum possible
pure class A1 power.

(9) Calculate class A1 power from graph voltage readings.
Class A Ea swing = Ea - Ea minimum for class A1
= 400 - 240 = 160Vpk.


Class A1 power = 
2 x (Ea - Ea min) squared / RLa-a
=
2 x 160 x 160 / 4,000 = 12.8 Watts.


The class A1 Va-a Vrms swing may be calculated
= Class A1 Ea pk swing x 0.707 x 2
= 160Vpk x 0.707 x 2 = 226.2 Vrms.
Class A PO = Va-a squared / RLa-a = 226.2 x 226.2 / 4,000 = 12.8 Watts.

It is difficult to get exact agreement for class A1 PO from (8) and (9) because
of slight errors when drawing graphs. The difference between the graphical
results and pure calculated class A is not important. In practice, the transition
between class A and class AB is not at an abrupt transition because the cut
off behavior of each tube is not linear. The actual load each tube sees
while working in class AB varies between class A load of RLa-a / 2 and
RLa-a / 4, and the real load line is actually a curved line between the
two load values. For design purposes the load lines are kept straight,
and tubes are considered perfect devices. The variations of shape of Ra
curves for differing Eg1 and the uneven spacing between Ra curves for
equal changes in Eg1 show the 6550 to not have perfect characteristics
and in fact the Ra ohm value and transconductance vary considerably.

The class AB1 maximum power largely depends on the shape of the Ra
curves and the position of the curve "knee" for Eg1 = 0V, ie, about where
point B is located. In practice, this knee in Russian made 6550 is often more
toward the right at Ea = 100V and Ia = 340mA, and max class AB1 power
will be less than 50W, and will most likely be so if the tubes operate with UL
taps or CFB windings have more than 25% of total primary turns.

There are very few accurate sources of Ra curves for Russian tubes and
I have never seen a reliable set of curves for Chinese power tubes. Once
you have built an amp and become familiar with beam tetrodes pentodes
and
triodes, then all this load line analysis will not be such a puzzle.
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Anode heat dissipation.


PP Class A operation.


The RLa-a for maximum pure class operation is approximately calculated as
RLa-a = 1.8 x Ea / Iadc where 1.8 is a constant and Iadc is the idle Ia for
each tube.

For tubes in Fig 1, with Ea = 400V, Ia dc = 80mA,
RLa-a = 1.8 x 400V / 0.08A = 9,000 ohms.

Maximum PO = 0.5 x Iadc squared x RLa-a
= 0.5 x 0.08 x 0.08 x 9,000 = 28.8 Watts at clipping, sine wave.
Total Pda at idle = 2 x Ea x Ia = 2 x 400 x 0.08 = 64Watts.
For class A the power drawn from PSU does not change so
Total Pda at clipping, class A =  Ppsu - PO = 64 - 28.8 = 35.2W.
Pda per tube in class A maximum = 35.2 / 2 = 17.6 Watts.
So Pda in class A amps reduces as audio power increases and there
is never any need to check if Pda will exceed the Pda data for the tube.

In practice because music signals have a far lower average power level than
clipping level the 6550 remain at the same temperature with
barely changing Pda.


PP class AB operation.

The anode dissipation in class AB amps may vary considerably depending
on the RL and idle bias currents. The Pda max for a class AB amp will
always be highest when RLa-a is at a minimum value, ie, when RLa
is also at a minimum value as shown as straight line ABCD in Fig 1.

Fig 1 shows the load line ABCD for the class B RLa where Ea = 400V,
and RLa = 1k0, so that RLa-a = 4k0.

From the Fig 1 6550 anode curves, Ia maximum at point B = 0.34 Amps.
The Ea peak voltage swing at each anode = max Ia x RLa = 0.34 x 1,000
= 340Vpk. Va-a = 481 Vrms, PO = 57.8 Watts.

This maximum Ia is more than 4 times the Iadc at idle.

Therefore the Pda at powers above approximately 1/2 maximum possible
AB power is approximately equal to what is produced in a theoretical
pure class B amplifier where the Ia current waves in each tube are like
the positive 1/2 of a sine wave.

Power drawn from PSU, Ppsu, at more than 1/2 maximum PO may be
calculated as for a pure class B amp as :-
Ppsu = Ea x Peak Ia x 0.636.
= Ea x 1.8 x Va-a / RLa-a.

Total Pda, both tubes = Ppsu - PO.

Therefore
Total Pda = Ea x 1.8 x Va-a  -  Va-a squared
                           RLa-a
               RLa-a

= Va-a ( 1.8 x Ea - { Va-a } )

               RLa-a


In this example, Pda = 481 x ( 1.8 x 400V - { 481Vrms } ) / 4,000
= 28.7 Watts.
Pda per tube = 14.35Watts per tube, and this is less than 1/2 the
rated Pda for the tube, and therefore it is unlikely that as long as
the RLa-a is more than 4,000 ohms, and as long as there is no clipping,
Pda will never exceed the Pda rating for the tube.

But consider where Ea = 600Vdc, with RLa-a = 3,000 ohms
RLa for each tube = 750 ohms and the load line for 750 ohms
passes through the Ra curve for Eg1 = 0V at Ea = 250V.
Ea swing = 600V - 250V = 350V, so Va-a = 495Vrms.
Ouput power max = 81.6 Watts.
Total Pda = 495 x ( 1.8 x 600 - 495 ) / 3,000 
= 96.5 Watts = 48.25 Watts per tube.
The Pda is well above the rated Pda per tube = 42 watts and both
tubes will over heat and be destroyed by a continuous sine wave.

The use of RLa-a which is too low in ohm value with Ea much too
high for the RLa-a is not uncommon in many brand-name amplifiers.

The owner of any amplifier may make the mistake of connecting a 4
ohm speaker to an outlet labelled "16 ohms" because he thinks 4 ohms
is an easier load to drive than 16 ohms. Such a mistake reduces RLa-a
from say an ideal value of say 6k0 to 1k5, and he will be likely find
that his mistake causes clouds of smoke to be produced. The very low
load value also causes the damping factor to reduce, and THD and IMD
levels to increase to objectionable levels. So music and an amplifier
may be ruined by what seems to be common sense.

For more on Pda, go to my page at
anode-dissipation+waveforms.html

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To overcome all load matching problems I have seen in many sound systems,
the OPT should have Variable Load Matching. This means that the output tubes
and its OPT may be matched to any type of speakers of any impedance between
3 ohms and 16 ohms without having to find speakers to best suit the amp.
If you buy a car, you will hope the makers include a gearbox, because there
are some steep hills out there. The OPT is an "electronic" gear box which enables
the tubes to operate within their optimal Va and Ia range say between 5k0 and 8k0,
although the secondary load may be between 3 ohms and 16 ohms.

It would be indeed foolish of me to offer anyone an amplifier with a pair of 6550
with an OPT with a single impedance ratio of say 4,000 : 8 ohms only.
If we accept that most nominal "8 ohm" speakers have ZL at 6 ohms in their
main power band somewhere, then the OPT ratio should be
4,000 : 6 ohms at least. This allows speakers with Z above 6 ohms to be used.
But many people will buy "4 ohm" speakers and they will have a real need for
an amp to have a 4,000 : 3 ohm load match so any speaker above 3
ohms may be used.
Fig 2.
Graph of power out vs RLa-a, AB1 6550 beam
        tetrode.

Fig 2 graph shows the power output from 2 x 6550 in my above design example
plotted against load values. The OPT used is set for 8,000 : 6 ohms.
The power level is at clipping, or where THD < 2%.

Notice how you just don't get the same power ( limited by 2% THD ) for all
load values. While about 56W is available ( without smoke production ) if a 3
ohm speaker load is connected, with 6 ohms the power drops to 36W.
But 36W is usually more than enough for 99% of the hi-fi listeners I have met.
With a 6 ohm load, 3/4 of the power is pure class A and at all loads above 7.5
ohms all power is pure class A.

The 57W class AB1 amplifier I have described in my above example Fig 1 load
line analysis is really a 28W Class A1 amp.

In fact it is two amps within one, and paradoxical. Manufacturers are quick
to rave about their 57W class AB amps being much better than a weak sickly
class A amp capable of only 28 lousy watts.

But the marketing of anything *always* severely distorts the truth.

Suppose you have speakers rated for 88dB SPL per Watt at one metre.
A 28 amp can produce an SPL of 102dB, and with two channels you get 105dB.
A pair of 56W channels will increase SPL to only 108dB. To get a decent rise in
SPL to say 114 dB SPL, you would need two amps capable of 224W each.
And you'd need better speakers, and you'd need a good attorney to represent
you in a court case because you tried to damage the hearing and mental health
of all those living near you. The extra +3dB produced by exploiting the class AB1
potential of what is really a 28W class A1 PP amp is a very minor benefit.
I have attended at least three Sunday meetings of audiophiles and demonstrated
3 different types of amplifiers shown at my website using my amps and my own
speakers or Duntech Statesman speakers. On each occasion there were 30 men
gathered in a library venue with large size but good acoustics. The 8585 amp
with 4 x 6550 per channel sounded best, but they were quite well impressed
by a sample 5050 amp with 2 x 6550 per channel. They drooled over the sound
from my SEUL amps rated at 25W with a single 13E1 tube. The audiophiles
were there for hi-fi, and never to have their ears bashed to bits!

Nothing has much changed in 60 years about preferred SPLs for general hi-fi
listening levels and in RDH4 they say men prefer an average level of 88dB
while women prefer 84dB. These may be average levels found in an ideal seat
in front of a 40 piece orchestra. The likely difference between the real live
concert in a large venue and a hi-fi system at home will be the dynamic range.
There is no limiting of transients and no use of compression during the studio
recording production so the concert hall freshness and sparkle remains as pure
as it ever may be, but during the recording process, much of this is lost. 

We do have to draw a line somewhere with power. I once re-engineered a
Leak 20 for a customer who wanted to hear great things from tubes through
his Duntech Sovereign. These were large floor standing speakers similar to
AR9 but made a heck of a lot better. They have ZL from 3 to 4.5 ohms
and 87dB/W/M sensitivity. Well, the old Leak gave a pretty good 12 watts
per channel, class AB1 from pairs of EL84, and maybe 8 watts of pure class
A max. The Leak 20 has adjustable output load matching and can be set for
4 ohms but it still lacked the power to drive the Duntech properly with low
THD. But in 1960 many speakers had sensitivity at 96dB/W/M.
The Leak 20 would sound much happier driving Tannoy dual concentric
speakers.

Today's speakers usually need a tube amp capable of 25W of class A1.
If the amp is a PP type, then often the AB1 capability is twice the maximum
class A ability. For this you will need at least 2 x 6550 or KT88, or 4 x 6L6,
EL34, KT66. 12W class AB1 from a pair of 6BQ5 is just not enough,
and the 12W in pure class A PP triode with 2 x 6L6, KT66, EL34, will
also struggle, although do a better job than 2 x EL84 in UL.

The above example calculations for class AB1 use of 6550 is approximately
valid for use of the Ultralinear or Acoustical connection.
Slightly less maximum AB1 power is available compared to pure beam tetrode
mode. The same class A power is available.

Subjectively, the sound from UL or Acoustical mode of operation is better
than pure beam tetrode or pentode and THD measurements tend to confirm
what we hear.

For pure beam tetrode or pentode, say with 2 x 6550, 20dB global NFB is
needed even when there is class A1 with an OPT of 8k0 : 6 ohms.
28W of pure class A will give THD = 2% without global NFB
and 0.2% with global NFB, and at 2.8W we may expect 0.06%.
Lower THD figures are possible with UL and Acoustical and with less
global NFB and usually the mix of harmonic products are less complex
and thus more able to be tolerated by our ears.


The effect of NFB on output resistance can be explained similarly as I
explain in my page on 'LOAD MATCHING 2.' for load matching to
Single ended beam tetrodes.
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Simple class A load lines......
Fig 3.

graph-6550ge-beamtet-8ka-a-loadlines-eg2-350v.GIF
Fig 3 shows the load line for pure class A1 single ended or push pull tubes
and in this case for 6550 beam tetrode.

To draw the load line for the pure class A load,
(1), draw horizontal line to right thru 2 x Ia at idle ie, at 160mA.
(2) Plot point A on Limiting Ra line aka diode line.
(3) Plot point Q at Ia idle dc = 80mA and at Ea = 400V.
(4) Read Ea minimum on graph, vertically below point A, = 30V.
Calculate Ea swing = Ea at idle - Ea minimum = 400V - 30V = 370V.
Calculate Ea maximum = Ea at idle + Ea swing = 400V + 370V = 770V.
Plot point B on Ea axis at 770V.
(5) A straight line may be drawn through points AQB.
The ohm value of this line for RLa
= Ea change / Ia change = Ea Peak swing / Ia = 370V / 0.08A = 4,625 ohms.

For two tubes in PP, RLa-a = 2 x RLa = 9,259 ohms.

Power output for RLa-a = 2 x Ea pk swing squared / RLa-a
= 2 x 370 x 370 / 9,250 = 29.6 Watts.


Calculating RL by approximate formula for class A1
beam tetrodes or pentodes,

SE RLa = 0.9 x Ea at idle / Ia at idle
= 0.9 x 400 / 0.08 = 4,500 ohms.

PP RL a-a = 1.8 x Ea / Ia
= 1.8 x 400 x 0.08 = 9,000 ohms.

where 0.9 and 1.8 are constants Ea is Vdc at idle from anode to cathode,
Ia is idle Idc of ONE tube.

If only Ea is known because we have an available power transformer
to give B+ between say +300Vdc and +500Vdc, and we know what
maximum Pda is permissible, then Ia dc = Pda / Ea.

Also, it may be useful to calculate.......

RLa-a = ( 1.8 x Ea squared ) / Pda 

RLa-a = 1.8 x Pda / Ia squared.

Ia at idle = 1.342 x square root of ( Pda / RLa-a )

Ea at idle = square root of ( RLa-a x Pda ) / 1.342.
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Some further calculations and notes about gain and Rout for Fig 3.

Max class A1 load swing = 370Vpk, RLa-a = 9,250 ohms, PO = 29.6 Watts.

Va-a = 523Vrms. To achieve the Ea minimum peak anode Ea swing,
Eg1 must swing from -20V to -10V, or a change of +10Vpk.
But while one tube has Eg1 swing = +10V, an equal Eg1 change but
of opposite phase will be applied from the driver stage to the other tube
grid of -10Vpk. The curves in Fig 3 indicate the Ea change will to
Ea max = 680V, well short of the 770V predicted. In fact considerable
distortion occurs and it is only able to reduced to negligible levels by
applying a total of 20dB of external loop negative feedback.
This is most commonly done by a global NFB loop.

Examination of Fig 3 shows that considerable THD without any NFB
will occur with the RL for one tube = 4,625 ohms, and that approximate
2H % at clipping = 100% x ( AQ - QB ) / [ 2 x ( AQ + QB ) ]
where AQ = Ea idle - Ea min for Eg1 swing required,
QB = Ea + Ea max where Eg1 swing is the same for AQ swing.
In this case, 2H % = 100% x ( 370 - 280 / [2 x ( 370 + 280 ) ] = 6.9%
The 2H is mostly cancelled out by PP operation, but there will be
about 3%  of 3H at clipping. 20dB of global NFB will reduce this to
about 0.3%.
There will be inevitable OPT winding losses of perhaps 3% with a
pure class A load, so with NFB the PO will be 29.6 Watts
theoretically calculated less a total of approximately 5% = 28 Watts.
Examination of the voltages fed to the two x 6550 grids when 20dB global
NFB is used will show considerable THD in the grid voltage because to
gain a large reduction in THD there must be a considerable error
signal included in the grid drive signal to produce the linear output signal.

The measurements of relative signal voltages within the amp at clipping are
somewhat different to what is found at say 2.8 Watts when THD is very
low even without GNFB, when Ea pk swing is about 1/3 maximum.

The 6550 voltage gain may be read from the graph at low THD where
Eg1 changes from -20V to -17V, to give Ea change = -125V, so voltage
gain = 125 / 3 = 41.66. To get Ea change = +/- 370Vpk, gain is lower and
approximately 11Vpk rms is required, = 7.8Vrms at each grid.

Let us suppose the driver amp has an LTP with 6CG7 with a single ended
6CG7 input so that input and LTP driver gain = 16 x 8 = 128 times.
To produce 15.6Vg-g the Vgk at V1 input = 0.1218Vrms. 
Let us suppose the OPT has a ratio of 9,250 ohms : 6 ohms so ZR = 1,541
so TR = 39.26, and let us neglect losses and suppose Va-a max = 523Vrms
and Vo to 6 ohms = 13.3Vrms.
 
Open Loop Gain without GNFB = V0 / Vin = 13.3 / 0.1218 = 109.1.

For 20dB of GNFB, the OLG must be reduced by factor of 0.1, so Vin
with GNFB = V1 Vgk x 10 = 0.1218 x 10 = 1.218vrms. The required
NFB voltage wanted at the V1 cathode = Vin with GNFB - Vg-k
= 1.218 = 0.1218 = 1.096Vrms.

The fraction of the output fed back, ß, = 1.096Vrms / 13.3 Vrms = 0.0824

Rout of the amp with FB applied  =                    Ra-a                             
                                                                   ZR x ( 1 + [ A" x {µ/TR} x ß ] ) 

Where Ra-a is the anode to anode resistance of the output tubes,
ZR is the output transformer impedance ratio,
A" is the gain of the stages preceding the output tubes,
µ is the amplification factor of the output tubes,
TR is the primary to secondary turn ratio of the OPT = square root of
OPT ZR, ß is the fraction of OPT secondary voltage fed back to be
"in series" with the input voltage to V1.

At the working point at Q Ra = 25k, so Ra-a = 50,000 ohms ( approx ).
OPT impedance ratio = 9k25 : 6 ohms = 1,541 : 1,
A" = 256,
µ = 180,
TR  turn ratio = sq.rt 1,541 = 39.26,
ß = 0.0824

In this case, Rout
 =                            50,000                                  =  0.657 ohms
      1,541 x ( 1 + [ 128 x {180/39.26} x 0.0824 ] )

Damping factor = RL / Rout = 6 / 0.657 = 9.12. This is close to 100%
valid for class A operation at low levels, before class AB operation begins.
Class AB operation with lower RLa-a will disturb the calculations.

Increasing GNFB by 6 dB would reduce Rout by 1/2 and double the
damping factor, and require Vin = 2.4Vrms, somewhat high.

If the amp had a load of 3 ohms at the secondary, at low levels the
amp remains in class A so the equations are valid. All equation factors
remain the same so Rout remains at 0.657 but damping factor is reduced
to 3 / 0.657 = 4.6, barely high enough. At high levels with the 3 ohm load
the tube action becomes mainly class AB and effective TR increases
therefore increasing Rout. There is a reduction of gain in the OP stage
and the amount of applied NFB is reduced. Both factors increase
THD maximums.


In the case UL connected pair of 6550 with UL taps at 43%, each 6550
has
Ra = 4.0k, µ = 24. The class A gain with RLa = 4k6 is approximately 12.8.
The output stage gain reduction achieves better linearity, and for the same Va-a
of 523Vrms, each grid input voltage will be 20.4Vrms approx.
With UL, Eg2 = Ea = 400V, then Eg1 will be -35V approx, and thus the grid
drive voltage will not generate grid current. With the same input drive amp
using 6CG7 and gain = 128, the V1 Vg-k will be 0.319Vrms. For class A UL,
14dB GNFB may be used so input voltage is 5 x 0.318Vrms = 1.6Vrms.
so VFB = 1.6 - 0.318 = 1.27Vrms, and with Vo = 13.3Vrms, ß = 0.095.

UL Rout  =                               8,000                                =  0.615 ohms
                     1,541 x ( 1 + [ 128 x {24/39.26} x 0.095 ] )


Damping factor with 6 ohm load = RL / Rout = 6 / 0.615 = 9.75.

Such a DF is more than required unless a 3 ohm load is going to be used,
which would be foolish.

Larger reductions of effective Ra-a in the OP stage are possible with the
Acoustical connection. Even 10% CFB as used in Quad-II reduces Ra-a of
KT66 from 76k0 to the same as triodes, approximately 3k2, a reduction of
more than x 1/20.
I  prefer the Acoustical with CFB option, and when using
about 20% of the primary for CFB, the drive voltage to an output grid is
raised to about 75 Vrms, or about 7 times the pure beam tetrode drive voltage
so then the driver amp needs to have more idle current and low distortion ability.
But I think the end result sounds better with the CFB and mild global NFB.

The previous samples are approximate calculations of what to expect when you
build and measure an amp.


For more about NFB within triodes, and theory about beam tetrodes with an
Equivalent Model for calculation gain of UL connected tubes,
go to 'Basic Tubes 4'.


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