# How Does a Vacuum Tube Work

### Two key concepts for understanding how a vacuum tube works are thermionic emission and charge attraction and repulsion.

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The theory behind the operation of a vacuum tube is based on a concept known as thermionic emission.

In addition to this concepts including the attraction and repulsion of opposite and like charges play a large part in the operation of vacuum tubes / thermionic valves.

Understanding these concepts provides the basis behind understanding how a vacuum tube works.

## Thermionic emission

The first concept needed to understand how a vacuum tube works is that of thermionic emission.

Electrical conductivity of metals results from the fact that there are free electrons moving around the material and not attached to any definite molecule. Although there are equivalent numbers of holes so that the overall charge remains balanced, these electrons roam freely around the material.

If these electrons are to leave the surface of the material, work needs to be done to overcome the attraction within the material.

The energy required to overcome the forces holding the electrons within the material can be supplied in a number of ways. One of these is to heat the material and in this way the electrons receive additional kinetic energy. At a sufficiently high temperature, some electrons will have sufficient kinetic energy to escape from the surface of the material. This is thermionic emission of electrons, and it is this phenomenon that is at the core of how a vacuum tube works.

The process of thermionic emission from a material has many similarities with that of evaporation from the surface of a liquid. In the case of molecules in a liquid, the ones that escape and evaporate have sufficient energy to escape the retraining forces of the liquid, and the number escaping increases with increasing temperature. It can be considered as essentially the same process in which the energy the electron must give up corresponds to the latent heat of vaporisation in a liquid.

## Electron emission

In looking at how a vacuum tube works it is also necessary to consider the effectiveness of the way in which electrons escape from the surface.

The number of electrons emitted from the heated material per unit area is related to the absolute temperature as well as a constant 'b' that is a constant indicating the work an electron has to do to escape the surface.

As a result it is possible to derive an equation for the current leaving the surface:

$I=A{T}^{2}{\epsilon }^{\left(}-b/T\right)$

Where:
I = current measured in Amperes
A = a constant for the type of emitting material
T= temperature in degrees Absolute
b = work required for electron to leave surface

## Electron emitters - cathode materials

It is necessary to reach temperatures in excess of 500°C, dependent upon the material, for the number of electrons leaving the surface of the material to become appreciable. When working with temperatures of this order, it limits the materials that can be used on the cathodes of vacuum tubes.

There are a few favoured emitters that are used within vacuum tubes:

• Tungsten:   Tungsten provides one of the most robust forms of filament for a vacuum tube, particularly when very high anode voltages are used. However its drawback is that its emission efficiency expressed in terms of amperes emission per watt of heating is not as high as other emitters like thoriated tungsten and oxide coated emitters.
• Thoriated tungsen:   Thoriated tungsten is widely used in vacuum tubes and consists of tungsten containing 1 to 2% of thorium oxide. Vacuum tubes / thermionic valves using cathodes with this coating give electron emission at temperatures of between 1500° and 1600°K. Vacuum tubes using thoriated tungsten must have a very high degree of vacuum otherwise the positive ions produced by ionisation of gases in the envelope will seriously affect the emission.
• Oxide coated emitters:   Vacuum tubes using this form of cathode coating have layer of a mixture of barium and strontium oxides coating the surface of the cathode. When properly activated they emit electrons profusely at a temperature of around 1100° to 1200°K. Oxide coated emitters are widely used because they give more emission per watt of heating than any other type. One drawback is that the emitting surface is easily poisoned by impurities. Vacuum tubes using oxide coatings are used for most small vacuum tubes / thermionic valves using voltages up to a few thousand volts.

Although, normally vacuum tubes are indirectly heated these days, this form of heating is less efficient than the directly heated option. As a result, some specialist tubes or valves that use tungsten or thoriated tungsten filaments sometimes use direct heating techniques.

## Space charge

One important aspect of vacuum tube theory is the space charge.

The electrons flowing between the cathode and the anode form a cloud of electrons and this is known as the "space charge". The space charge tends to repel electrons leaving the cathode, forcing them back. However if the potential applied to the anode is sufficiently high then the space charge effect will be overcome, so that electrons will flow toward the anode. In this way electrons are able to move across the vacuum within the glass envelope of the vacuum tube / valve, the circuit is completed and current flows.

As the potential is increased on the anode, so the current increases. Eventually a point is reached where the space change is completely neutralised and the maximum emission from the cathode is attained. The only way in which the electron emission fromt the cathode can be increased is by increasing the cathode temperature. This increases the energy of the electrons and as a result it allows further electrons to leave the cathode.

Although all areas of a vacuum tube have a space charge, it is of particular importance in the cathode region as it determines elements including the maximum emission.

As other electrodes are added into the evacuated envelope, the space charge concept can be applied to the whole operational area.

The space charge concept plays a crucial role in determining the flow of current in any thermionic device.

## Child's Law

Child's Law, often also called the Child-Langmuir Law was first proposed in 1911 and it forms a key elements within thermionic valve or vacuum tube theory and how a vacuum tube works.

Child's Law states that the space-charge limited current in a plane-parallel vacuum diode varies directly as the three-halves power of the anode voltage and inversely as the square of the distance d separating the cathode and the anode.

$J=\mathrm{Ia}/S$

Where:
J = current density in Amperes per metre squared,
Ia = anode current,
S = anode surface area in square metres

Child derived this equation applicable to vacuum tube theory in 1911 for the case of atomic ions. These have much smaller ratios of their charge to their mass. Irving Langmuir extended the basic law when he published the application to electron currents in 1913. This extended it to the case of cylindrical cathodes and anodes. It is for this reason that the law is sometimes referred to as the Child-Langmuir Law.