Contents of this page :-
Fig 1. Graph of 6SN7 Ra curves with load lines for 47k and 32 k.
How to find Ra for a given working point and plot loadlines in steps 1 to19.
Comment on THD and other topology outcomes.
Fig 2. Scanned Ra curves from Samuel Seely, 1958.
explanations about the Ra curves.
About gain with CCS load and µ.
6SN7 THD with CCS load calculations from data curves.
After you have carefully read all of 'Tube Operation 1', you might have a chance
to understand loadlines drawn for 1/2 6SN7 in Tube-Op-1, with dc load = 47k and
ac load of 100k, B+ = +300Vdc.

Fig 1. Ea vs Ia for 1/2 6CG7.
Here we have a anode Ra curves for various Eg1 and for a 6J5 which was
developed in 1930s for use in many instruments where industry, medical and
military applications needed a linear amp. 6J5 is a single small signal indirectly
heated triode with good linearity if the load line is a CCS, but here I have the
loadline on curves for total RLa = 32k, because in many audio amps this might
be the typical set up.
Two such triodes were put inside one octal base tube to make a 6SN7, and later
there were smaller anode versions used to to make the 6CG7, with 2 triodes and a
mini 9 pin base. 6FQ7 seems to be identical. Siemens and Telefunken versions of
6CG7 may have been The Best ever made, ie, the "best sounding", but Australian
production by AWV has always seemed to me to be equal to any Sacred Tube
made in Germany or USA. Demand for electronics mushroomed after WW2, and
to satisfy demand the trend was from octal based tubes to miniature 9pinand 7pin,
and here in Oz the same anode+grid+cathode structure for 6SN7 was re-packaged
into a mini 9 pin tube to make 6CG7. It was used many thousands for telephone
exchanges, TV sets, and 101 other items, and some were used best quality audio
But many ppl used 6SN7 which was made in vast numbers with many left over after
WW2, and sold to the public with 807 at Army Disposal stores which traded into the
Those brave ppl who made their own Williamson amps heard the sonic benefits of
the 6SN7. It is still a popular tube among DIY brethren.

I am unaware of the exact degree of accuracy of the curves, but experience tells me
they are accurate enough to base design topologies upon, and to ascertain the behavior
of a signal triode. The method mentioned in text in .gif says how to plot loadlines.
The same steps can be used for any other set of Ra curves for any other triode.

From the loadlines, we can see Vg = 9.8Vpk-pk. Va = 141Vpk-pk, and gain = Va / Vg
= 141 / 9.8 = 14.38.

The horizontal line for constant 3mA shows Ea = 36V for curve Eg 0.0V, and
Ea 351V for Eg -16V.
Total Ea swing with CCS load 351V - 36V = 315V. µ = 315 / 16 = 19.69, and if we
determined µ at 3.4mA, maybe µ would be slightly more at say 20.0.

The Ra determined from graph line G-Q-H = 13.65k.
The formula for gain A = µ x RL / ( Ra + RL ) and from graph we might get
A = 20 x 32k ( 13k6 + 32k ) = 14.04.
There will be differences between the gain calculated with assumed µ and Ra,
the gain calculated from loadlines, and gain observed from a number of samples of tubes.
6SN7 made in USA, Australia, UK, Europe or Russia. But they will all have such similar µ,
Ra and gm that the general design principles apply to all.

The largest THD product is 2H, with 3,4,5,6H at low levels. THD is at a maximum
where the load is low, say 1k0, where the loadline is nearly vertical. THD is low where
load > 10 x Ra, say 150k, and lowest where load line is a CCS, ie, a constant current
source, which is a horizontal loadline. THD for CCS can be 1/4 for clipping level Va for
RLa = 32k.

After scanning the original triode curves I was able to tidy up the paper image in MSPaint.
Further down this page I have an available blank .gif image of curves for those wanting to
draw their own loadlines.

Anyone could print a copy and use a ruler and pencil to draw the load lines, but I prefer
the screen of the PC to draw a line, no paper is needed, and thus we might save the
forests and reduce greenhouse gases.

How to plot load lines for a triode and find out the Ra, µ and gm of the triode :-

Each curve represents non linear anode resistance Ra for varying Ea & Ia values for set
values of Eg1 grid bias voltage.

(1) Choose B+ you want to use between +250Vdc and +450Vdc for intended use.
For preamps and power amp input stages :- +250V to 300V is adequate for Idc feed
using resistance. Idc feed from CCS can have lower B+, because Va is often less than
10Vrms, so the Ea can be 140V with B+ 200V, and if the CCS using a bjt occupies 15V,
then peak Ea swing can be +/- 40Vpk. Iadc can be between 3mA and 8mA without worrying
about the RLdc value. The anode RLa is determined by the following C coupled R at next
 stage which may be 220k, so that RLa = Ra x 16, and THD will be vert low.
But for nearly all triodes where no CCS is to be used, the total RLa should be at least
2 x Ra, with C coupled load at least 2 x RLdc.
For this example loadline analysis, I have chosen 47 for RLdc, and 100k for C coupled
load, and total RLa = 32k. this is above 2 x Ra, and I predict THD = 4.6% at 50Vrms
maximum output.
The THD rises at a slightly increasing rate up to clipping where rate of increase is suddenly
exponential. The THD at 10Vrms could be about 0.8%, and at 1Vrms for a preamp,
about 0.08%. With CCS and RLa say 220k, expect THD at 10Vrms = 0.3%, and at 1Vrms
= 0.03%, and sound will be amazingly good.

For driver stages of output tubes the B+ can be +450V which allows conditions such as :-
RLdc = 50k, 5W, Iadc = 4mA, C coupled load = 180k, Total RLa = 39k.
Max Ia pk swing = +/- 3.7mA to make Ea pk swing = 144V, and you should just get 100Vrms.
Expect THD = 7%. But at 10Vrms it may be a benign 0.7%. If there are 2 triodes used in a
balanced amp with a common Rk = 13k7 to a -100Vdc rail, then 2H reduction is almost all
eliminated but there may be 3% 3H. But at 10Vrms, the 3H may measure < 0.25%, and is a
good result.

See my pages where 6CG7 have been used for input tubes and driver tubes in preamps
and power amps.
Pda max for all uses of 6SN7 should be less than 1/2 of rated Pda in data sheets.

(2) Calculate the total RLa for 6SN7 including capacitor coupled bias resistance of next
amp stage.
Total RLa = RLdc parallel to C coupled R = 47k // 100k = 32k.
Calculate max Ia if tube is a short circuit with 32k connected = ( Ea / total RLa ) + Ia at Q
= ( 140V / 32k ) + 3.4mA = 7.78mA.
Plot point C at 7.78mA x 0V.
Calculate max possible instantaneous Ea if tube is open circuit = Ea + ( Ia at Q x total RLa )
= 140V + ( 3.4mA x 32k ) = 248.8V.
Plot point F at 248.8V x 0.0mA.
Draw straight line between C and F. This should pass through point Q; if not, you have made
a mistake. The red line C-F is for total RLa line of 32k.

(3) Draw a straight line through Q which is parallel to tangents drawn through nearest Ra
curves each side of Q. This line is the Ra at Q. This scarlet line from Q crosses point H at
94V x 0.0mA. Continue the line from H through with about equal distance to H at 180V x 6.3mA.
Calculated the resistance value of line = Ra = G-Q-H = Difference of V / Ia
= ( 180V - 94V ) / 6.3 = 13.65k.

(4) Estimate Ea pk swings. Plot D on line C-Q-F where it intersects Ra curve for EG = 0V.
D is at 63V x 5.7mA.
Calculate Ea negative swing = Ea at D - Ea at Q = 63V - 140V = -77V.
Determine Ea positive swing for the same change of Eg change for negative Ea swing.
Eg swing = -4.9V, at Ea max, Eg swing is to -9.8V.
Plot point E on line C-Q-F where Eg = -9.8V. E is at 204V x 1.3mA.
Calculate Ea positive swing = Ea max - Ea = 204V - 140V = +64V.

(5) Calculate 2H distortion.
2H % = 100% x 0.5 ( difference in +/- Ea swings ) / sum of +/- Ea swings
= 50% x ( 77V - 64V ) / ( 204V - 64V ) = 50% x 13 / 141 = 4.6%.

The single 1/2 6SN7 would be barely able to drive an output tube in an SE amp
which had a bias voltage = -50V where 35Vrms or 100Vpk-pk is needed for such
an output tube such as KT88 in UL or triode mode.

However, the 2H of 6SN7 would tend to cancel the 2H of any UL or triode SE
output tube. But some IMD products are produced in the cancelling process so
it is better to try to use the 6SN7 with both halves paralleled and with higher Ea
and Ia and with a higher number of ohms for RLa to achieve a bigger possible
Va swing and much better linearity. The driver tube for an output stage should be
able to make at least 1.5 times the maximum Vg signal applied to output tube to
produce grid current. This means that where you have 20% CFB windings with
say 6550 or KT88, each output tube may require 75Vrms or over +/- 100Vpk.
This becomes difficult for tubes like 6SN7 and a better solution is to employ 6BQ5
in triode and Ia at least 12mAdc. For SE drivers, a choke of at least 60H is used in
series with say 4k7 between B+ = +350Vdc, and Ea may be +300V, and Ea swing
can be 140Vrms without resorting to bootstrapping of the anode RLdc load. See my
300W amps for details.

Usually power amps need about 1Vrms for clipping, and for normal listening levels
an average of only 0.1Vrms is needed. For high output CD players and possibly
sound cards from PCs or USBs et all, there may be no need for any preamp.

A 6SN7 preamp triode may well have gain = approx 14 With low level inputs
such as 1980s FM tuners the Vo level may be 200mV and some amps need 2Vrms
for clipping. Therefore a preamp with gain = 10 is needed.
Usually, lowest preamp noise is where the gain pot follows the preamp which is used
for low level input. 0.2Vrms input is boosted to 2Vrms, then both tube noise and signal
is reduced by gain pot for normal listening levels and SNR is best. If the gain pot is
before the preamp, the preamp noise is not attenuated and the SNR is -20dB worse.

See my pages on pre-amplifiers and power amplifiers for more about ideal set ups for
6SN7/ 6CG7 etc.

Load lines for cathode follower tubes may be done exactly the same way as for a
gain tube with anode RL and grounded cathode. The CF tube with fixed Ea and load
placed between cathode and 0V operates exactly the same way as the plate loaded
gain triode. CF Gain is below unity, and THD is very low.

There are better ways to make a gain stage than by just using one gain.

Fig 2.
This is the tidied up image I scanned from Samuel Seely's book from 1958.
The .gif should download easily and be able to be opened in MS paint and worked on
as a BMP monochrome image, ie, just black and white. All sorts of load lines can be
drawn, and magically un-drawn if you make a mistake!

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