SMALL SIGNAL AMPLIFIERS
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
developed in 1930s for use in many instruments where industry,
military applications needed a linear amp. 6J5 is a single small
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
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",
production by AWV has always seemed to me to be equal to any
made in Germany or USA. Demand for electronics mushroomed after
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
into a mini 9 pin tube to make 6CG7. It was used many thousands
exchanges, TV sets, and 101 other items, and some were used best
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
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
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
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
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
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
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 =
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
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
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 =
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
= 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
output tube. But some IMD products are produced in the cancelling
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
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
say 6550 or KT88, each output tube may require 75Vrms or over +/-
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
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
an average of only 0.1Vrms is needed. For high output CD players
sound cards from PCs or USBs et all, there may be no need for any
A 6SN7 preamp triode may well have gain = approx 14 With low level
such as 1980s FM tuners the Vo level may be 200mV and some amps
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
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
This is the tidied up image I scanned from Samuel Seely's book
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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