This page explains how to set up single ended output beam tetrodes in tube amplifiers using the 6550 and KT88
working in pure class A beam tetrode mode or with 43% UL screen taps.

This page has the following content :-
Description of the operation of the beam tetrode with cut-away sketch by RCA.
* Fig1. Graph of anode resistance curves for GE 6550A beam tetrode with screen supply = +350V.
* Fig 2. Graph of anode resistance curves for GE 6550A beam tetrode with screen voltage = +350V plus 3 load lines and
calculated results for gain, power output and second harmonic distortion.
* Fig 3. Graph of anode resistance curves for GE6550A beam tetrode but with screen supply = +200V.
* Fig 4. Graph of anode resistance curves for GE6550A with one load line for 3.5k and  calculated gain, power and 2H .
Explanation of the effects of NFB application for 6550 beam tetrodes
Formulas for NFB and output resistance.
* Fig 5. Graph for power output for single 6550 beam tetrode vs anode load value.
Choosing the OPT ratio.
* Fig 6. Graph of 6550 anode resistance curves for 6550 in UL mode with 43% screen taps.
Calculated gain, power output and 2H for 4 different load values.
Data for Ra, µ and gm for UL and comment on the effects of NFB and distortion outcomes.

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The beam tetrode is basically a four electrode vacuum tube with beam forming plates
The electrodes are cathode, k, control grid, g1, screen grid, g2, Anode, a, and two beam forming/confining
electrodes or metal plates.

The structure of a beam tube is obvious when examining a 6550,
KT88, or 6L6. The sketch only shows part of the tube internals. RCA was short of enough ink in 1935 to draw the whole of the diagram. The plate, or anode as otherwise more correctly named is a kind of open ended box surrounding the whole center grid structure, not just acting on one side as shown, and open at the top and bottom to allow heat from the cathode to more easily radiate up and downwards.
Electrons in fact radiate from each side of the cathode.
There are in fact two beam confining electrodes or plates located
adjacent to the ends of the elipse shaped grids. The two beam
confining plates are connected to the cathode and have the low
cathode voltage potential and each plate repels electrons to
increase the density of the electron flow towards the anodes so the
electrons are in the form of concentrated beams from the cathode.
This beam forming action prevents secondary emissions from the anode and gives the wanted predictable beam tetrode characteristic curves which are very much like those of a pentode.
The beam tetrode was invented to overcome the necessity of using power pentode tubes which were first patented in Europe.
The advantages of the beam tetrode and power pentode allow for about twice the audio or RF output power compared to triodes which have a similar anode dissipation.
The beam power tube or power pentode can be used with its screen grid connected to the anode to make the tube operate as a triode. In the case of the 6550, the maximum anode dissipation rating is 42 watts, and the theoretical maximum amount
of audio power from a single tube in class A1 =  18 watts in beam power mode, but only about 10 watts in class A1 triode.
In practice, nobody should ever have a single 6550 set up with Pda = 42 watts at idle because the tube would run too hot
and have a short life and about 35 watts maximum is more sensible for combined screen and anode dissipation
so that max power in beam tetrode = 15 watts, and in triode about 8 watts.
It is possible to extract more power in triode by operating in class A2, and get perhaps 12 watts but I feel there are not many benefits because of the higher THD and extra circuit complexity, ( another tube stage ) to cope with the grid current at above the class A1 limiting threshold.

Not many people will have access to a supply of NOS GE6550A or NOS KT88 which are very similar. So their new tube supplies of will be from Russia, China or eastern europe.

The New Sensor Corp sold me a large batch of EH 6550 tubes in Feb 2002. The latest update of this website was done in March 2006, and I have not had any reports of any early failures tubes in that purchase.
The working characteristics of these recently made Russian tubes appear to be equal to NOS samples of the same tube type
such as the renowned GE6550A, and can be generally be used as replacements in all amps requiring 6550 or KT88.
I also recently measured Sovtek KT88, which gave identical test results to the EH6550.
Sovtek or EH 6550 or EH KT88  from Russia all appear to me at least to have exactly the same internal physical structure and electronic beam tetrode data parameters of
Ra = 19,000 ohms, Gm = 10mA/V, and µ = 190 at Ea = +400V, Ia = 60mA, and Eg2 = +350V.    

Anode curves for GE 6550A are similar to EH6550.....
Fig 1.

These curves are for GE6550A but typical for any 6550.

If we look along the Ia = 100mA line we see that for a change in grid voltage of 1.5V
there is an Ea change = 350V, so µ = 350 / 1.5 = 233.
If we look along the Eg = -17V line we seee that for 350V of Ea change there is an Ia change of 18mA.
so Ra = 350 / 0.018 = 19,444 ohms. Therefore gm =  12mA/V.

At Eg = -10V, the Ra = 10k and µ = 100 so gm = 10mA/V.

The anode curves are more crowded together vertically at the bottom of the graph indicating a large change in
Ra, µ and gm between Ia = 50mA and Ia = 300 mA.

Here are some load lines and analysis for loads of 1.75k, 3.5k, 7k....
Fig 2.

Here we have the 6550 loaded with 1.75k, 3.5k and 7k.

For a full explanation of how to understand and plot load lines, go to my load matching (2) page on using single beam tetrodes as triodes, and read the section on understanding and plotting load lines.

For Q point1, Pda = 31.5watts, one can calculate the 3 outcomes in Vg, Va, gain, power and second harmonic distortion.
1.75k  :-  Vg = 11Vrms, Va = 156Vrms, gain = 14.2, power = 13.9 watts, 2H = 19%.
3.5k    :-  Vg = 6.7Vrms, Va = 189Vrms, gain = 28.2, power = 11.6 watts, 2H = 12%.
7.0k    :-  Vg =  4.7Vrms, Va = 216Vrms, gain = 45.9, power = 6.7 watts, 2H = 3.7%.

The "best" RL = 3.5k, and at 1 watt, at Va = 60Vrms, and THD is about 3%.

From these rather poor figures  we can see that 2H  is dreadful at low RL and at high RL it falls, and may fall even further
to 0% and then the phase of the 2H increases again but with the opposite phase.
But the figures for 2H don't include most of the other harmonics which are significant and numerous.
Here are curves for GE6550 with screen voltage a lot lower = 200V :-
Fig 3.

Sometimes the beam or pentode tubes produce better curves so lower distortion with screen voltage
lower than anode voltage.
Here is a 3.5k load plotted on the above curves :-
Fig 4.

With a lower screen voltage, The operating point can be Ea = 350V, Ia = 90mA for Pda = 31.5 watts as in the
case where Eg2 = 350V.  The load is 3.5k .
The outcome at maximum power with no NFB :-

Vg =  6.7Vrms, Va = 185Vrms, gain = 27.6, power = 9.8watts, 2H = 8.3%.
At one watt, THD = 3%
If there was 20dB of global NFB we could expect THD at 9.8 watts to become about 1%
and 0.3% at 1 watt. Maximum power would be boosted to about 13 watts because the anode V swing
would be increased to about 600V pk to pk from the 523V shown above.
There is an increase in power output which is proportional to the increase in V swing squared.

No matter what load one tries to use with a beam pentode, the load that gives a healthy power output also
produces high THD even at low levels, because THD is approximately proportional to
output voltage, so that where you have 9 watts of output, then at 0.9 watts the output voltage is
0.316 times the level for 9 watts.

I would never use any beam tetrode pentode in single ended mode unless I could have ultralinear taps or cathode
feedback windings on the output transformer, or just use plain triode connection.

Let us suppose the OPT ratio chosen was 5k : 6 ohms, or 833 : 1, so that if  if there is a dip in speaker Z below the nominal 6 ohms to say 4.3 ohms, the load seen by the anode = 3.5k as shown above. The high Ra of the tetrode = approximately
17k ohms at the working point Q. ( it could be more ).
The Ra of the tube measured at the secondary =  17,000 / 833 = 20.4 ohms = output resistance without NFB.

Let us now explore the effect of 20 dB of global NFB on an SE tetrode amp.

Where 20dB of global NFB is used, the gain without NFB is reduced by a factor = 0.1.

Consider the SE 6550 in tetrode in the above load line sample with 4.3 ohms load on the OPT secondary.
we have 6.7Vrms grid signal to make 9.8 watts into 4.3 ohms = 6.5vrms. Say have a 12AX7 used to drive the 6550
and it has a gain of  say 67. Therefore 0.1Vrms is needed at the 12AX7 grid to produce 6.5 Vrms at the load.

Therefore gain without NFB, called open loop gain = 6.5 / 0.1 = 65.
Suppose we reduce the open loop gain by applying 0.9Vrms of NFB to the 12AX7 cathode via a low resistance divider network from the OPT secondary speaker connection, using a typical divider of R1 = 293 ohms plus R2 = 47ohms.

This will reduce the open loop gain to 6.5 which is known as the closed loop gain.
ß, the fraction of the output fed back = R2 / ( R1 + R2 ) = 47 / 340 = 0.138.

To confirm what we have done, A', gain with NFB = A / ( 1 + [ A x ß ] ) = 65 / ( 1 + [ 65 x 0.138 ] ) = 6.5.

But if there was no load on the tetrode output tube, open loop gain, A = ( gain of 12AX7 x µ of 6550 ) / OPT turn ratio
 = 67 x 190 / 28.9 = 440.
If open loop gain was 440, and ß remained at 0.138, A', closed loop gain = 440 / ( 1 + [ 440 x 0.138 ] ) = 7.12.
The amount of gain reduction is much greater where A is much higher; the change in A' of between 6.5 and 7.12
is not much, so tubes with varying gains will have much more even and constant gains when NFB is used.

With a load of 3.5k, the feedback resulting from ß = 0.138 gives 20dB of gain reduction, but without any output load at all there is a gain reduction 440 to 7.12 = 61 times, = 36 dB of effectively applied NFB. This amount of NFB **will** make the amp become unstable at both ends of the audio spectrum and is a reason why steps must be taken with beam tetrodes and pentodes to use zobel networks to reduce gain and phase shift in the open loop character below 20Hz and above 20kHz.

When 20dB of global NFB is applied with the 3.5k RL the open loop distortions are also reduced by slightly less than
20dB. 2H, which is the main harmonic product will be indeed reduced about 9 times to 0.92% at about 9.5 watts and 0.3% at 1 watt. However, since the 2H is fed back there is a slight production of 3H by means of intermodulation and there is greater spectral complexity of the harmonic content after FB is applied then before, even though the level is much reduced.

The effect of intermodulation where only 10dB of NFB is applied around a tetrode amp is all the more greater
with an increase in 3H that could make the sound worse. So when applying NFB, use enough where distortion is high to begin with as its the case with a tetrode amplifier.

The calculation of output resistance is more difficult to calculate because we are need to take into acount the µ of the output
tube.  To reference our calculations to the secondary connection,
the µ of the output tube at the OPT secondary = µ / OPT turn ratio
In this case it is 190 / 28.9 = 6.57.

The output resistance of a tube amp can also be calculated if you know
1, voltage gains of the input and driver stages,
2, µ of the output tubes,
3, turn ratio of primary to secondary which is the unloaded voltage ration between P and S windings,
4, the anode resistance, Ra of one output tube at the Q point.
5, winding wire resistance of the primary and secondary windings of the OPT.

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

Where Ra is for the one output tube,
Rw total is the sum of OPT primary winding wire resistance and ZR x secondary winding wire resistance.
Allow Rw total to be 10% of the rated primary load if the Rw measured is unknown.
TR is the turn ratio of the OPT, or unloaded P to S signal voltage ratio at 1kHz, or square root of the exact known ZR.
ZR is the output transformer impedance ratio which is the turn ratio squared,
A" is the gain of the stages preceeding the output tube/s, ie, V at output tube grid / Vg-k of the input tube,
µ is the amplification factor of an output tube/s,
ß is the fraction of OPT secondary voltage fed back to be "in series" with the input voltage to V1.

For example in this case we have :-
Ra-a = 17,000 ohms,
Rw = 10% of primary RL of 3.5k = 350 ohms,
TR =  28.86 : 1
ZR = 5,000 ohms : 6 ohms = 833 : 1,
A" = 67
µ = 190
ß = 50 / ( 50 + 600 ) = 0.138
Rout' = closed loop output resistance at the secondary output terminals

This is a good result and could be compared to the result with the 6550 connected in triode where Ra = 900 ohms,
µ = 7.33, and the OPT had the same ratio.
But for 20dB of applied NFB with 3.5k anode load, ß must be increased to 0.73
and with the same driver tube with its gain 67.....

Rout', triode, =                                      900 + 350                           = 0.11 ohms, about 1/4 of the tetrode case.
                                    833 x  ( 1 + [ 67 x 7.33/28.9 x 0.73 ] )

We can conclude that about 17dB would be enough global NFB for the tetrode amp to get Rout = about 0.5 ohms.
The triode amp would need only 8 dB to achieve the same low Rout.

The power levels shown are without any NFB and at the anode with no OPT losses, and could be approximately 20% more with about 20dB of NFB, to give a net 10% increase allowing for an OPT with 10% winding losses.
With NFB the 2H and other distortions are reduced to less than 2% and voltage swings on the load are
less limited.

The OPT for the above Ea and Ia condition should have the lowest expected speaker load matched to 3.5k, so if the speaker's nominal Z is 6 ohms, allow for a dip in Z to say 4.3 ohms so the OPT impedance ration = 3.5k : 4.3 ohms which is 5k to 6 ohms, ie, 833 : 1
The Rout before NFB is about 21 ohms and with 20 dB of global NFB it will be approximately 0.33 ohms as calculated above. A trioded 6550 will also give Rout = 2 ohms  without any NFB but with 12 dB of global NFB the Rout
will be about 0.6 ohms.

Single Ended Ultralinear could be another option to use.
The data here is for a GE 6550A with 43% screen taps.
Fig 6.

If I were to start with an Ea = 400V and Ia = 80mA for Pda = 32 watts,
RL =  ( 400 / 0.08 ) - 300 = 5,000 - 300 = 4,700 ohms.
If the  operating  idle point is 350V x  90mA as in the above  graph, we get
RL = ( 350 / 0.09 ) - 300 = 3,588 ohms.
 

With 43% taps, the SE tetrode characteristics change to the following :-
Ra =  2.0k, µ = 15.4, gm =  7.7mA/V at Ea = 350V,  Ia = 90mA, Pda = 31.5 watts.

The performance outcomes are :-

1.2k    :-  Vg = 17Vrms, Va = 92Vrms, gain = 5.4, power = 7.1 watts, 2H = 15%.
2.0k    :-  Vg = 17.7Vrms, Va = 131Vrms, gain = 7.4, power = 8.5 watts, 2H = 12%.
3.6k    :-  Vg = 17.7vrms, Va = 170Vrms, gain = 9.6, power = 8 watts, 2H = 8.3%, ( 3.6k load line not shown )
4.7k    :-  Vg = 17.7Vrms, Va = 191Vrms, gain = 10.7, power = 7.8 watts, 2H = 5.5%.
11.7k  :-  Vg  = 17.7Vrms, Va = 218Vrms, gain = 12.3, power = 4.0 watts, 2H = 1.7%
The "best" RL = 4.7k, and at 1 watt, at Va = 60Vrms, and THD is about 1.5%.
The use of global NFB increases the maximum power output up to 20% without more severe THD.

The advantage with UL is that although the 2H remains fairly high, there is much less other harmonics to worry about
and the tube behaves much like triode but without the limitation of the Eg = 0V limiting the Ea minimum as much.

The load for maximum power is about 3.6k, and so nominal speaker loads should match about 5k.

Therefore an OPT would have a ratio of  say 5k : 6 ohms which has an impedance ratio = 833 : 1.
This allows for any dip in speaker load impedance to 4 ohms without hugely increasing distortion.The UL Ra when measured at OPT secondary = 2,000 / 833 = 2.4 ohms. 12dB of NFB will reduce this further to about 0.8 ohm and nearer to a triode with the same global NFB and OPT ratio.

If we plotted a load of 4,700 ohms through the Quiescent point Ea = 400V and Ia = 80 mA, we would
get a swing of about 0.9 x Ea = 360V peak giving 13.7 watts maximum in theory. In practice we may get
13 watts when pushed into low THD by  NFB application. If you plot low loads less than 2k the phase of the output 2H is like triode, and 2H diminishes to zero at some load above 2k then 2H increases as load increases but phase of 2H is opposite.
The SEUL connected tube has slightly less 2H than triode or about 1% when power output is 1/10 the maximum.

The use of distributed loading in the OPT with 20% of the primary turns in a cathode feedback winding
and with the screens taken to a fixed voltage of about +270V will give much better linearity than triode or UL screen taps.
Such an arrangement has voltage NFB applied relationships between grid and cathode and between screen and cathode.
20% CFB with fixed screen supply voltage Eg2, is the equivalent of having 20% UL taps but with about 10dB of series voltage NFB between cathode and grid when a 4.7k load is used.
Thus THD < 2% THD at 9watts. This oversimplifies what is occuring in the tube, because there are two paths of NFB,
one via the screen to cathode interface and the other via the grid cathode interface. There is still some odd numbered
harmonic products in the THD but they are much reduced below the levels occuring with pure beam tetrode.
The results using EH6550 ( or EH6CA7 ) in my SE 35 watt amps with CFB indicated that more could be achieved
with CFB than just UL screen taps and still have gain about equal to triodes. The SE 35 watt amps have remarkably
low THD and low Rout and with only very minimal global NFB. See my page on SE35 amps. 

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