| ← Previous: Physical Construction | Next: The Triode → |
If plate voltage is applied to a cold tube, then an electric field is set up between the plate and the cathode. The voltage in this field increases linearly in the distance between the two electrodes. This is shown by the red line in Figure 6. Once the cathode is heated up and starts emitting, the electrons themselves alter the situation, because the electron carries a negative charge. Although this is very small (1.602·10-19 Coulombs), there are a lot of them, and the emitted electrons themselves contribute to the electric field in the space between the electrodes, modifying it from the straight line shown in red in Figure 6. The green line shows the effect using a simple analysis, ignoring initial electron velocity (Child's Law), while the blue line shows the true state of affairs when initial electron velocity is considered.
The term space charge is used to refer to the charge due to the electrons occupying the inter-electrode space. The space charge plays a crucial role in controlling the flow of current, which is at the heart of the controlled amplifying action of the vacuum tube. There are several myths and misunderstandings concerning space charge. It is often implied that it exists only in the immediate region of the cathode, and there are references to the space charge region. It is true that the space charge in this region has particular importance, as we shall see later, but it is present in the whole inter-electrode space. Another source of confusion is the space charge tubes which were developed in the 1950s, for use in car radios. To allow them to operate effectively on the 12V supply in the car, without needing a higher voltage, they used an unusual configuration of grids to limit the reduction in plate current due to the space charge. These are now of interest only to collectors.
 |
| Figure 6: Charge distribution between cathode and plate |
The Child-Langmuir Law
The number of electrons depends on the current flow - the higher the current, the greater the number of electrons and therefore the greater the charge. Since the cathode feels the influence of the plate through the negatively-charged electrons between them, the increasing current reduces the attractive force of the plate until the two reach a balance. At this point of balance, the effective field at the surface of the cathode is reduced to zero. Moving away from the cathode, the electrons accelerate. The accelerating electrons spread out, just like cars on a freeway moving away from a traffic jam, reducing the space charge so that the field increases. This is illustrated by the green line in Figure 6, which shows what happens inside a tube when current is flowing under normal operating conditions (under this analysis).
The mathematics of this is beyond the scope of this article, but it is relatively straightforward to obtain the Child-Langmuir law (sometimes referred to simply as Childs law), as it applies to a diode:
| $I=\dfrac{2.335\cdot 10^{-6}AV^{\frac{3}{2}}}{d^{2}}$ | where: | $V$ = plate voltage $A$ = cathode area (cm2) $d$ = distance between cathode and plate (cm) |
This is the well-known ³⁄₂ power law of the relationship between current and voltage. Note also the bottom of the equation: the current drops with the square of inter-electrode distance. This is why designers need to keep the physical dimensions of the tube as small as possible.
This equation (and the green line in Figure 6) is based on a simplification, that all of the electrons are emitted with zero residual energy. We have already seen that in fact they are emitted with a distribution of energy, and later on we look at the effect this has.
This law strictly applies only to infinite flat electrodes. In reality of course the electrodes are finite, but in a practical tube the effect of this is relatively minor. A similar equation applies to cylindrical electrodes, which still involves the ³⁄₂ power of voltage, and in fact it can be shown that any electrode configuration will involve this factor.
One implication of this law is that the current flowing depends only on the strength of the field due to the plate in the immediate vicinity of the cathode. This field must be just strong enough to counter exactly the space charge set up by the resulting current. The field elsewhere serves to accelerate the electron flow but plays no role in determining its magnitude.
Saturation
The current emitted by the cathode under normal conditions is far in excess of the current that passes to the plate. The emission of an oxide cathode is upwards of 0.5A/cm2. Even for a power tube, the ratio between the emitted current and the operating current is at least 10. The maximum plate current rating that appears in the specification for a tube is based mainly on considerations of heating, and in pulse operation can safely be exceeded (as it was in TV sweep circuits, for example).
If all of the emitted electrons do pass to the plate, then the operation is completely different. The plate current becomes practically independent of the plate voltage. In a triode, the grid no longer has any control over the current. This mode of operation is called thermal saturation (or just saturation), in contrast to the normal mode which is sometimes called space-charge limited. Under these conditions the full effect of the field due to the plate is felt directly at the cathode, since the space charge (which does still exist) is no longer strong enough to counter it. In fact, the saturated current does increase a little with plate voltage, especially with oxide cathodes, because the increasing field strength can pull more electrons out of the surface of the cathode. This is called the Schottky effect.
It must be stressed though that in audio, no practical vacuum tube circuit operates in saturation, even for short periods. (There are uses in other areas. One is the noise diode, which is deliberately operated with a low heater voltage so that emission is low, and saturation occurs continuously. Another is in high-current pulse switching).
| ← Previous: Physical Construction | Next: The Triode → |
No comments:
Post a Comment