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Secondary Emission
When an energetic, fast-moving electron hits a metal surface, the impact dislodges some of the other electrons and causes them to be emitted. An electron arriving at a 250V plate has an energy of 250eV, whereas the metals work function means that only around 4eV is required for an electron to be emitted. This phenomenon is called secondary emission, and occurs each and every time an energetic electron arrives. Under normal conditions, the plate is the most positive thing around, and these secondary electrons are simply attracted back to the plate where, having only a little energy, they are re-absorbed without provoking any further emission. This is benign and has no effect on the electrical operation of the tube, and is indeed unmeasurable
Secondary emission only becomes a problem when the emitting surface is not the most positive thing nearby. In this case the emitted electrons are captured by the electric field and form a secondary current between the two electrodes. For example, if the grid of a triode is made positive rather than negative, and more positive than the plate, so that electrons flow directly to it, then the secondary electrons will be attracted to the grid, causing a flow of current away from the plate
Secondary emission - or more accurately, secondary current flow - is almost never a good thing. It occurs unavoidably in the tetrode (as described below) and is the principal reason why tetrodes have been replaced by pentodes. It was exploited in photomultiplier tubes, as a way to multiply a very feeble initial current. There was also a tube in the late 1930s, the Philips EFP60, which used secondary emission from a target electrode as a way to increase the Gm, but it proved difficult to build predictably and was not successful. The problem is that although secondary emission can be measured for a particular metal, and in principle allowed for, in practice it is heavily affected by surface contaminants and the like. It cannot therefore be used as a reliable element of a tubes operation
Vacuum
In theory, the inside of a tubes envelope is a vacuum. In practice, a perfect vacuum is unachievable, and a certain level of residual gas has to be accepted. The pumps that are used to evacuate tubes can typically get down to about 10-7 mm of mercury, or about 10-10 of atmospheric pressure. However once the tube is sealed, gas can still get into the space inside it. First, the glass-to-metal seals around the pins or lead-out wires are not perfect, and allow small amounts of air to pass. Secondly, a certain amount of gas is adsorbed at the surface of the metals, mica and glass inside the tube. Under the high vacuum, this gas is slowly released, particularly if the surface is raised to a high temperature. This is the main reason why allowing the plate of a tube to overheat is bad. It results in a sudden release of gas, faster than the getter can absorb it, which interferes with the tubes operation and can rapidly result in destruction of the cathode
An essential part of the structure of all tubes is the getter, the silvery coating to be seen somewhere on the glass envelope. It is generally made of barium, which when hot reacts with gases, taking them out of circulation as soon as they appear. As the tube ages, the getter is gradually used up. Anything resulting in a serious gas leak will exhaust the getter quickly, and this can easily be seen because its appearance changes from silvery to white. In manufacture, the getter is placed inside a special container, often a small cup which can be seen attached to the internal structure close to the getter location on the envelope. Once the tube has been exhausted by a pump, and sealed, the getter is fired either by passing an electric current or using an induction heater. Thus the film is deposited on the envelope
If the vacuum is not perfect, and we have seen that it never is, then some gas molecules remain inside the tube. When an energetic electron hits such a molecule, it generally knocks one or more of the electrons out of it, resulting in a positively charged ion. This is then attracted in the opposite direction from the electrons, i.e. towards the grid and the cathode. The majority of these hit the cathode. Here their energy is able to dislodge the surface atoms, particularly in oxide cathodes, which is called cathode stripping. The gradual erosion of the cathode surface is one of the principal factors limiting the life of small tubes. This is why tubes should ideally not have plate voltage applied until they are warm, since in this way the getter has a chance to deal with gas molecules which have appeared since the tube was last operated
The chances of an individual electron colliding with a gas molecule are very small. In a new tube an electron could travel around 10 kilometers on average, before having such a collision. However, because of the large number of electrons involved in carrying the current, the number of such ionisation events is large around one billion per second for a small tube in typical conditions, with a good vacuum (10-7 mm Hg).
Tube testers estimate the vacuum in the tube by measuring the negative grid current under determined operating conditions. The higher the current, the more gas that is present. In a new tube with near-perfect vacuum, this current is much less than 1 μA, but if a tube starts to lose vacuum it becomes measurable.
Interelectrode Capacitance
Any closely-spaced conductors have a capacitance between them, and the electrodes of a tube are no exception. In a triode, the capacitance from the grid to the plate and the cathode respectively could in principle be worked out from the tube dimensions. Typical values are a few pF for each of them, for small-signal tubes. Large-signal tubes have higher values, simply because of the larger electrode areas.
There is also capacitance between the lead-out wires. This is very small, but it can be enough to cause RF oscillation if this is not damped by resistors close to the tube base.
There is also a capacitance between the plate and the cathode, but this is reduced by a factor equal to µ from what the normal capacitance formulae would give. Typical practical values are 0.5-1pF, which is largely due to the lead-out capacitance.
Finally, the very close spacing between the cathode and the heater packed inside it also results in capacitive coupling, typically around 1pF. This allows noise and RFI, in particular, to couple from the heater supply into the signal, and vice versa.
The most common amplifier circuit is the common cathode, but the interelectrode capacitance causes a particular problem in this configuration at higher frequencies. As the grid voltage rises, the plate current increases and hence the plate voltage falls by an amount equal to the amplification of the circuit. But this falling voltage is capacitively coupled back into the grid, leading to the Miller Effect in which the effective value of the grid-plate capacitance, as seen by the driving circuit, is multiplied by the gain of the circuit.
This is a big problem but RF, but it can be significant for audio too, depending on the circuit design. Whereas a value of say 4pF would have little effect, at audio frequencies, the Miller Effect results in a value of several hundred pF.
The cascode input stage design, with two tubes effectively in series, nearly eliminates Miller Effect, at the cost of an extra tube element. At very high frequencies, for example in a UHF tuner, a grounded grid circuit must be used.
Grid Current
Since the grid has no physical connection to anything (as the circuit symbol shows), it is natural to think of it as being electrically isolated. In fact, this is not the case, because of the flow of electrons and ions inside the tube
Current flow to and from the grid arises for two reasons. The most obvious is when the grid is positive, which causes it to attract electrons. Less obviously, when the grid is negative, it attracts positive ions resulting from collisions between electrons and gas molecules. These cause the grid to become less negative. It is because of this effect that the grid must never be left truly floating but must always be connected through a resistance, typically for a small tube not more than 1MΩ. Without this, the voltage of the grid will gradually creep up, reducing negative bias and increasing current through the tube and leading to a runaway which, at worst, will destroy it through overheating. As mentioned above, tube testers measure negative grid current as a proxy for gassiness.
At the right voltage, these two currents cancel out. This normally occurs at around 0.5V (depending slightly on plate voltage), which is slightly positive relative to the virtual cathode. If the grid is simply left disconnected, it will float at this voltage, and the plate current will correspond to this level of bias. This is the basis for a so-called leaky-grid detector, since operatiopn in this region is very non-linear.
Positive grid current is deliberately used in some cases, for example in high-µ transmitting tubes. When it occurs, Child's Law gives, not the plate current, but the sum of the plate and grid current. This is because total current is controlled by the field in the immediate vicinity of the cathode, which is due to the combination of the two other electrodes. To calculate the actual plate current (and hence also grid current), it is necessary to know how much of the electron stream flows to each of the two electrodes. This is given from the following formula:
| $\frac{I_{p}}{I_{g}}=\delta\sqrt{\frac{V_{p}}{V_{g}}}$ | where: | $\delta$ = current division factor |
The current division factor is slightly greater than the shielding ratio of the grid. If grid current curves are available for a tube, it is easy to determine its value from them.
Unfortunately this tidy formula only gives the value for the primary current. Once the grid is more positive than the plate, secondary emission will start to occur, resulting in a secondary current flow from the plate to the grid and reducing the effective grid current. This is, for all practical purposes, unpredictable. Depending on the tube, the secondary current may even exceed the primary current, typically at around 30-50V. This results in a second stable voltage for a disconnected grid at the point where the primary and secondary currents exactly balance
Positive grid current results in heating of the grid, for the same reason that the plate gets hot (i.e. due to the kinetic energy of the arriving electrons). Small tubes are not generally designed for this, but power tubes and especially tubes designed for positive grid operation have substantial dissipators attached to the grid structure.
Overheating of the grid is bad for two reasons. Firstly, since it is not designed to run at a high temperature, it does not have any way to retain its tension as the metal expands. This results in changing geometry and in the worst case melting or a short to the cathode, which is instant death. Secondly, the grid is generally contaminated by oxide from the cathode, and if it gets hot then it will start to emit electrons like the cathode, resulting in a substantial secondary current
Close Electrode Spacing
Because $G_{m}$ increases inversely with the square of the grid-cathode distance, tube designers have always been under pressure to reduce this distance. However, if it falls below the grid pitch, the design assumptions of the triode start not to apply. The field is no longer uniform at the cathode, but rather varies, becoming less negative between the grid wires. In fact, if the separation falls below 0.6 of the pitch, the $G_{m}$ starts to fall again. As a result, the evolution of vacuum tube technology is marked by ever-finer grids, so that this relationship can be maintained. Fremlin [Frem39] describes the theory which applies when the grid is closer to the cathode than its pitch.
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| Figure 10: Zero-volt potential contour as tube approaches cutoff (dimensions in cm) | |||
Figure 10 shows how this applies to a 6SN7, which being an older design does not have especially close spacing. At -5.3V grid potential, the whole cathode is contributing to the plate current. As the grid becomes more negative, "inselbildung" starts - the parts of the cathode directly under the grid wires are in a negative field. By -10V less than half the cathode is still contributing. At -11.4V, the whole cathode is seeing a negative potential, and the tube is truly cut off, i.e. there is no plate current. It can be shown that the effect of inselbildung is to replace the $\tfrac{3}{2}$ power in Child's Law by a $\tfrac{5}{2}$ power. Thus at high currents and small grid voltage, the tube obeys a $\tfrac{3}{2}$ power, but as the grid is made more negative and current reduces, this gradually turns into a $\tfrac{5}{2}$ law. This is a major reason for the tuck under that plate curves show at large negative grid voltages.
So far this is purely a question of proportion, and not of the absolute size of the tube. Recall however that the space charge creates a virtual cathode typically about 0.1mm ahead of the physical cathode, which further reduces the effective distance to the grid. This distance is independent of the tube geometry. It is 0.1mm whether in an early tube with 2mm from cathode to grid, or in a 1950s design where it may be 0.2mm or less - which places the grid only slightly ahead of the virtual cathode. In fact the virtual cathode is no longer a straight line. Since it is further from the physical cathode at lower current, it will approach the grid wires even closer, forming something close to a mirror image of the 0V potential contour. (This ignores the sideways velocity of the electrons. As far as I know the impact of this has never been analysed in detail, probably because the required computing power only appeared after the tube was considered obsolete). The extreme case of close spacing is the WE417A (or 5842), which achieves a record value of $G_{M}$ for a small tube (25 mA/V) by very close construction. For this tube, at low currents the virtual cathode actually reaches the plane of the grid. From this point all of the classic mathematical description of triode operation becomes completely irrelevant.
From a practical point of view, at least as far as audio is concerned, the moral of all this is to operate tubes at as high a standing current and as low a bias level (i.e. closer to zero) as is possible for the circuit to operate correctly, so as to keep operation well into the $\tfrac{3}{2}$ power part of the plate curves and hence reduce distortion, paticularly higher-harmonic distortion
Directly Heated Tubes
Most of the physics behind directly-heated tubes is the same as for indirectly-heated tubes, but there are some differences. First, there is the question of the effective area of the cathode. An accepted formula for this is to use the length of the filament times twice the filament-grid distance [Spang48, p189]
The most significant difference arises because the voltage along the filament is not constant, but varies from one end to the other by the applied filament potential. Although this potential is small, it must be remembered that the effective plate voltage as seen at the cathode (filament) is also small. For example, a 300B operating under quiescent conditions of 350V and 90mA, with 60V on the grid, has a potential as seen at the cathode of around 15V, against a filament voltage of 5V. At the negative extreme of grid voltage, modulated by the signal, this effective voltage will drop close to or even below 5V
When the effective plate voltage is less than the filament voltage, only part of the filament contributes to the plate current, i.e. the part which is still more negative than the filament. Furthermore, the current varies along the filament. The effect of this is that the current becomes dependent on the $\tfrac{5}{2}$ power of the effective plate voltage, rather than the $\tfrac{3}{2}$ power. As the plate voltage increases beyond the filament voltage, there is a gradual transition between the $\tfrac{3}{2}$ power and the $\tfrac{5}{2}$ power, which is approximately given by the formula [Dow37]:
| $I_{p}=PV_{eff}^{\text{ }\text{ }\text{ }\text{ }\tfrac{3}{2}}\left[ 1-\tfrac{3}{4}\left( 1+\tfrac{1}{\mu} \right)\dfrac{V_{fil}}{V_{eff}}{} \right]$ | where: | $P$ = perveance $V_{eff}$ = effective plate voltage $V_{fil}$ = filament voltage |
It is this shift from a $\tfrac{3}{2}$ law to a $\tfrac{5}{2}$ law which explains the distinctive tuck under observed in the plate curves for filamentary tubes at high negative grid voltages and low currents. Substituting the above numbers for a typical 300B, the plate current will be reduced by about 25%.
It has been observed [Bench99] that distortion can be measurably reduced with filamentary tubes by lowering the filament voltage to the lowest possible value consistent with avoiding saturation. In fact, in a filamentary tube with close cathode-grid spacing, at low currents the law will follow an even higher power, in theory $\tfrac{7}{2}$.
Using AC rather than DC for the filaments does not significantly reduce this effect. At any given instant, even with AC heating, there is a potential gradient along the filament (except for the brief moment when the filament voltage passes through zero). Some of the time it is greater than the equivalent DC voltage, and some of the time it is less, but taken through the whole AC cycle the net effect is substantially the same.
Contact Potential
Any two different metals placed in contact with each other generate a potential difference. This is the underlying principle of all batteries, as well as the thermocouple. This difference is due to the different energy levels of the electrons in the two metals, and is called the contact potential of the two metals. The reasons are similar to the work function which determines electron emission, although the two are not the same. In fact, this effect applies even if the two metals are not in contact with each other, applying in this case to the electric field between them. Thus the grid and cathode of a tube, typically made of nickel and barium/strontium oxide respectively, have a small contact potential, which serves to change the effective grid potential. This contact potential is typically less than 0.5V
Transit Time
The electrons must take a finite amount of time to travel from the cathode to the plate. This time is referred to as transit time, and is sometimes invoked to explain various phenomena relating to audio. Transit time did indeed become of practical importance when tubes were first used to build VHF and UHF equipment, and it ultimately sets a limit to the frequencies at which they can usefully operate (in the region 1-2GHz). The transit time can be calculated to be around 1nS from cathode to plate, which at audio frequencies is clearly not relevant.
Multi-Grid Tubes: The Tetrode
The triode was the first amplifying device to be built, but at radio frequencies it suffers from a grave disadvantage because of the Miller Effect, which gives it a large effective input capacitance in the conventional common-cathode circuit. To avoid this, the tetrode was invented, having a second grid (the screen grid) between the triode grid (called the control grid in multi-grid tubes) and the plate. This grid is connected to a positive voltage close to the plate potential, but grounded to high frequencies through a decoupling capacitor. This results in an electrostatic shield which reduces the effective control grid-plate capacitance to a very low value
A secondary effect of the screen grid is to reduce dramatically the influence of the plate voltage on the current flow, since the cathode is shielded from the plate by not one but two grids, and their screening effect is multiplied. As a result, the plate curves of a tetrode are very flat, as seen on the right-hand side of Figure 11. This corresponds to a very high value of plate resistance, as compared to a triode
Some of the current from the cathode goes to the screen grid rather than the plate. The proportion depends on the shielding factor of the screen grid and on the relative potentials of the two electrodes, in much the same way as for a triode operated with a positive grid. It is typically 10-25%.
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| Figure 11: Plate and screen grid current of true tetrode (UY224) |
Unfortunately the tetrode suffers from a severe problem in practice. The left-hand side of Figure 11 shows that at low plate voltages, the plate curves are extremely non-linear. This is because of secondary emission from the plate. When the screen grid voltage is higher than the plate, electrons emitted from the plate by secondary emission, as it is struck by the energetic primary electrons, are attracted back to the screen grid instead of returning to the plate as occurs in a triode. As a result, a tetrode can only be used if the circuit design is such that this part of the plate curve will not be encountered. Hence, the simple tetrode has not been used, except for high-power transmitting tubes, since the 1930s. There has been no post-WWII small-signal tetrode produced in quantity.
The Pentode
The solution to the tetrode's problem was to introduce a third grid between the screen grid and the plate. Called the suppressor grid, this is always connected to the cathode and hence appears negative both to the plate and to the screen grid. By this means, secondary electrons emitted from both of these electrodes see a field which sends them back where they came from, regardless of the relative potential between the electrodes. Thus the problems of secondary emission are eliminated. The suppressor grid has no effect on the flow of current, since by the time electrons reach it they have been sufficiently accelerated by the screen grid that they simply pass between the grid wires. They are slowed down but not stopped by the grounded suppressor grid
Since the cathode is shielded from the plate by no less than three grids, the effect of plate voltage on current flow is negligible in the pentode, resulting in plate curves that are even flatter than for the tetrode
The Beam Tetrode
The beam tetrode exploits an alternative way of avoiding secondary emission problems, without the manufacturing complexity of using a third grid. It was observed in the 1930s that if the distance from the screen grid to the plate is large enough, the space charge of the electrons flowing in this region can depress the potential substantially without having an actual electrode. This is the basis of the beam tetrode. The reduced potential in this region serves the same function as the suppressor grid, causing secondary electrons to turn back to their origin and avoiding their effect on the electrode currents
To make this effect work in practice, three things are necessary. First, the electron flow must be confined to a narrow beam, otherwise the space charge spreads out parallel to the plate and the effect is lost. This is achieved by the beam electrodes, carefully shaped plates connected to the cathode and placed either side of the electron path between the screen grid and the plate. Second, the electrons must flow in clean sheets, which requires that the grid wires of the control grid and the screen grid be in line. This is not surprisingly a tricky manufacturing problem. Finally, the electrode dimensions and spacing must be carefully calculated
Although there are slight differences in the detailed operation of pentodes and beam tetrodes, for most practical purposes they can be considered as the same. Indeed, there are tube types which some manufacturers built one way, and others in the other way. Eric Barbour [Barb97] mentions that the EL84/6BQ5 was made in both ways.
Beyond the Pentode
To build an amplifier, nothing beyond the pentode is needed. But for some other special purposes, extra grids were added. In particular, hexodes (four grids) and heptodes (five grids) were used as frequency changers in radios and televisions. In these, one grid carries the RF signal, and one carries the oscillator frequency that intermodulates with the RF signal to generate the IF signal at a different carrier frequency.
Common frequency changers such as the ECH80/6AN7 put a triode in the same envelope, to provide the oscillator function.
With a heptode or even an octode (six grids), such as the EK90/6BE6, the oscillator could be combined in the same grid structure, avoiding the need for a separate tube or element.
The ultimate multi-grid tube was the EQ80/6BE7 nonode, with no less than seven grids. This was designed by Philips very specifically for use as an advanced FM detector, and seems not have had widespread use. It must have been very challenging to build, considering the tiny clearances involved.
Multi-Element Tubes
The electronic structure inside the glass envelope of a tube is generally quite small compared to the space available. It was therefore natural to put two or more such elements in a single envelope, especially where the combination satisfied some specific use case. The major limit to this was the number of pins available for the external connections. Typically each element had its own pins, with only the filament connection being shared between them.
Common combinations included:
- two independent triodes: 6SL7, 6SN7, ECC81/12AU7 and so on
- a triode amplifier and a pentode output stage: ECF80/6BL8, ECL80/6BE6
- a triode oscillator and a hexode frequency changer: ECH80/6BE6
Sometimes, certain connections were shared on a common pin. Often the cathodes would be wired this way, as in the ECL80/6BE6.
The ultimate multi-element tube was the ECLL80, which contained everything needed for a complete push-pull audio output stage: a triode phase splitter, and two beam pentodes for the output stage. This was only possible with some very clever pin-sharing, very specifically chosen for the intended use.
Color television greatly increased the number of tubes required, with three separate color video signals. In response, GE developed the Compactron tube in 1961, which used a new 12-pin base combined with a larger-diameter envelope. This allowed three triodes, or two pentodes, to be fitted into a single tube. However televisions rapidly moved to use transistors in the 1960s, so these had a very limited production life.
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