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 specific issues:

• 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 V:

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 Ua:

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 voltag
e

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 voltage.

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.

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 voltage.

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.

In all cases the anode current is less than 1mA, making it impossible to achieve the power output necessary to drive a loudspeaker.

Refs:

1 Izyumov, N., Linde, D. Fundamentals of Radio, Mir Publisher, Moscow 1976

2 Terman, F.E. Radio Engineering, McGraw-Hill Book Company, New York and London 1937