Rationale for the
use of thermionic valves with low HT.
Olivier Ernst, F5LVG Many thanks to the translator G0UCP
The decision to choose a
particular valve for operation with low voltage (HT) involves three
Variation in anode current as a
function of plate voltage
Variation of internal
resistance as a function of plate voltage
Variation of the slope as a
function of plate voltage.
I. Variation of anode current as a function of plate voltage.
(i). In diodes:
The current is the electrical charge that flows in a conductor in a given time:
I = dq/dt. In a diode valve, anode current is equal to the electronic
charge per unit of volume Rho multiplied by the speed of the electrons
Ia = RhoV. 
We have to calculate the electronic charge and the speed of the electrons.
The electronic charge corresponds to the electrons that escape from the
cathode under the influence of the anode voltage: If the cathode is hot
enough, the electronic charge is directly proportional to anode voltage
Ua. If anode voltage doubles, twice as many electrons leave the
cathode, so doubling the electronic charge. Conversely, if the voltage
Ua is zero, no electrons leave the cathode and the electronic charge is
zero. So Rho = k’Ua, where k’ is a constant that depends on the
physical characteristics of the valve. The kinetic energy of the
electrons (1/2mVsq ) is equal to their charge e multiplied by the anode
voltage Ua, so V = k’’sq rt Ua. Now we just substitute the values of
Rho and V to calculate the anode current as a function of the voltage
Ia = k Ua 3/2  where k is a constant which depends on the geometrical structure of the valve: The law of Child-Langmuir.
(Child's law states that the space-charge limited current (SCLC) in a
plane-parallel vacuum diode varies directly as the three-halves power
of the anode voltage Va and inversely as the square of the distance d
separating the cathode and the anode).
(ii). In triodes:
Triodes have a grid between cathode and plate. This grid, being close
to the cathode, has an effect mu times stronger than the anode on the
cathode current. The value of mu depends on the physical
characteristics of the valve and corresponds to the coefficient of
amplification. Cathode current thus depends on the voltages of both the
grid Ug and the anode Ua according to the following:
Ia = k[ Ug + (Ua/mu] 3/2 
As low power triodes frequently have a low value of grid voltage Ug
(i.e. less than 1 or 2 volts), one can generally assume on a first
approximation that the anode current Ia is proportional to the power
3/2 of the anode voltage.
II. Variation of internal resistance of a triode as a function of plate voltage.
The internal resistance Rp of a triode is equal to the relation between the variations of anode voltage dUa and anode current:
Ri = dUa / dIa = 1/(dIa / dUa)
In practice dIa / dUa is derived from anode current ( Ia) as a function of anode voltage( Ua). So
Ri = 1/ [(3k/2mu) ( Ug + (Ua / mu))1/2 ] 
So if the bias voltage Ug is weak, the internal resistance will be
inversely proportional to the square root of Ua, the anode voltage.
III. Variation of the slope of a triode as a function of plate voltage.
The slope of a triode is the relationship between coefficient of amplification and internal resistance: S = mu / Ri
So the slope of a triode (assuming that Ug is approximately zero) is proportional to the square root of Ua, the anode voltage.
IV. Effect of low anode voltage in a triode circuit.
In simple terms, when used with low anode voltage, anode current
diminishes according to the power 3/2 of the high-tension, the slope
diminishes (and the internal resistance increases) according to the
square root of the voltage. So a drop by 10 in the anode voltage leads
to a drop in anode current by 31 and slope by 3.1. It increases
internal resistance by 3.1.
Essentially, the choice of tube to use with low anode tension should favour a tube with a steep slope at low anode voltages.
V. Grid current and polarization.
When the cathode of a tube is heated it releases electrons. The
resulting electronic cloud means the cathode is surrounded by a
negative spatial charge. As it loses electrons, the cathode itself
becomes positive with respect to the negative electron cloud it has
released. A tube will only function if the electrical field due to the
anode at the level of the electronic cloud is above that of the
cathode, so negative electrons are drawn to the positive anode. If the
electrical field due to the anode is at a lower potential than the
cathode, then the electrons will be attracted to the cathode and anode
current will be zero. This explains why the tube only works above a
certain threshold anode voltage.
Manufacturers’ tables of tube characteristics never show tube
performance at low voltage. It was simply not considered a significant
specification. So certain tubes nominally of the same type, but from
different manufacturers may also perform differently at low voltage.
For example, of three batches of new 6K7 tubes obtained from three
different manufacturers, only two worked properly at an anode potential
of 12v, so experiment is still required.
VI. Threshold anode voltage
Under the influence of heating, electrons leave the cathode of a tube.
An electron cloud forming a negative spatial charge therefore surrounds
the cathode. Due to the loss of these electrons, the cathode becomes
positive in relation to this cloud, which contains negative electrons.
A tube only works if the electric field due to the anode at the level
of the electron cloud is greater than that of the cathode. The negative
electrons are then attracted to the positive anode. If the electric
field due to the anode is lower than that of the cathode, the electrons
are attracted to the cathode. The anode current is then zero. This
explains why the tube only operates above a certain threshold anode
Operation at a low anode voltage is never indicated in the
specifications of a tube. It was not a parameter to be met in the
specifications of a tube. Some tubes of the same reference, but from
different manufacturers may therefore have different low voltage
operation. For example, out of three batches of new 6K7 from three
different manufacturers, only two were operating correctly at 12 V
anode voltage. Experimentation is therefore still required.
VII. Which tubes?
In practice we should
use tubes with the highest possible slope. Below 12 volts, tubes in the
‘Noval’ series with a slope of 5 or 6 mA/V are usable (ECC81, ECC84,
ECC85, 6N3P...), but those with a slope near 12 mA/V give much higher
real gain (ECC88, ECC189, 6N23P...). Tubes with low slope are not
recommended. As regards power amplifier tubes, the EL84 remains a good
choice, but the output power obtained will still be very modest. Below
12V I strongly advise tubes with a frame grid, having a slope greater
than 12 mA/V. Among triodes, one might mention ECC88, ECC189 and
6N23P, but the Russian version, 6N24P is relatively cheap and works perfectly well on 12V. Similarly, for pentodes at 12V I advise either the EF183 or its Russian equivalent, 6K13P.
12V four tubes receiver
VIII. A forgotten technique: tubes with an accelerating grid, bi-grid or tri-grid space charge tubes
Space-charge-grid tubes (TERMAN)
One way to persuade a tube to operate below its threshold voltage
is to add an accelerator ‘space charge’ grid between the cathode and
the control grid. Connected to a positive voltage this produces an
electrical field at the level of the electron cloud which adds to that
of the anode. Although many electrons are captured by this grid, some
will pass through the mesh and be attracted on to the anode. Thanks to
this supplementary grid, the tubes can operate with a very low anode
potential of 12 or even 6V. This technique enjoyed some application in
France at the end of the 1920s as shown in various documents
gathered here (french). These were ‘bi-grid’ tubes, virtually impossible to find today. In fact they were very little used outside France.
It is possible to use a ‘modern’ pentode as a bi-grid tube. However
it is essential that the suppressor grid is not connected internally to
the cathode. The first grid receives a low positive voltage, the second
grid becomes the control grid and the third is strapped to the anode.
This results in a ‘bi-grid’ tube that will operate with a low anode
The third grid (suppressor) can also be connected directly to the high
tension source. If this grid has sufficient pitch, we have the
equivalent of a screen grid tube working at very low voltage.
One tube is particularly interesting in this application: the 6AS6 or its Russian equivalent the 6J2P.
Its heater draws little power, just 175mA at 6V, and the third grid is
a control grid. Consequently it offers the equivalent of a screen grid
tube if the third grid is connected to the ‘high- tension’ and of a
triode if it is connected to the plate. Experiment shows that the
optimal voltage for the heater when functioning in this mode is 4.5V (4
to 5V.). This tube still functions correctly at a heater voltage of 4V,
drawing less than 130mA. So 3 tubes with heaters wired in series can be
run from a 12V power supply. The voltage to be applied to the
first grid is approximately 2V at 5mA. Finally and notably, the
Russian version 6J2P is really cheap.
If you try other pentodes, it is essential that the third grid is not connected to the cathode.
all cases the anode current is less than 1mA, making it impossible to
achieve the power output necessary to drive a loudspeaker.
Izyumov, N., Linde, D. Fundamentals of Radio, Mir Publisher, Moscow
Terman, F.E. Radio Engineering, McGraw-Hill Book Company, New York
and London 1937