Part 3: Some vacuum tube theory

To understand the function of a thermal vacuum noise diode some general understanding of vacuum tubes is inevitable. In this (and the following) article I’ll try to work out the basic theories behind vacuum tube electronics, at least as far these affect the operation of vacuum noise diodes.

Electric current in vacuum tubes

tl;dr

Without going into any detail - many excellent books have been written on the matter, some of the more recently published (amongst others) are Jones [1], Blencowe [2], Honeycutt [3] a vacuum tube in essence uses two physical efffects:

1. generation of free electrons by heating electrically conducting material
2. applying electrical fields to control the movement of these electrons - thus generating electrical currents

History

Generally electric conductance is always dependent on free charge carriers, either electrons or ions. So the prime task for a vacuum device is to implement a source for charge carriers, usually in the form of free electrons. The electron source in vacuum tubes makes use of the Edison Effect, named after Thomas A. Edison, who in 1880 observed a strange effect in his newly invented electric filament (incandescent) light bulbs. Some of the bulb’s filament material (originally charred cotton, later tungsten) was sputtered against the inside of the bulb, slowly darkening it (especially towards the positive supply connector - remember, Edison used DC for all his experiments). It took some time to realize that this effect was due to the hot filament emitting electrons into the vacuum (and some of the filament’s material being torn out of the filament by these electrons, thus the darkening of the bulb). ¹)

Using a galvanometer Edison realized that the electrons emitted by the hot filament would flow to a another metal structure in the bulb once this structure was electrically positive relative to the filament and that no electron flow (i.e. current) would take place if this second structure was made electrically negative relative to the filament. Though thus having invented the vacuum diode, Edison saw no use in this effect and did not dig any further into the matter.

It was Sir Ambrose Fleming, British physicist working for the Marconi Wireless Telegraphy who realized that this effect could probably be used to demodulate (“detect” as it was called back then) radio waves, using the Edison bulb instead of the crystals used for this purpose. In 1904 he patented what since has become the vacuum diode. Independently US Engineer Lee de Forest invented (and patented) the vacuum diode in 1906. ²)

Vacuum Diodes

Basic Theory

Generally a vacuum diode is a two electrode device consisting of a heated electron source (the cathode) and an electron drain (the anode)³) in an evacuated (usually glass) cylinder. By heating the cathode the work function of the cathode’s material will be overcome and thus electrons emerge from the heated material building an electron cloud around the cathode, the space charge, also referred to as the virtual cathode due to the fact that it contains the area of the lowest electric potential. If no electrons (by whatever means) leave the space charge, the repelling effect of evenly charged particles will led to an equilibrium of electrons leaving the cathode due to heating power applied and electron recombining with the cathode due to being repelled by the negative space charge. Therefore keeping the cathode temperature constant will lead to a constant space charge.

But, by making the anode electrically positive relative to the cathode (i.e. by applying a positive voltage between anode and cathode) electrons are attracted towards the anode and an electrical current will start flowing from the cathode to the anode (reversing the voltage would lead to the anode repelling electrons due to it’s negative potential thus preventing any current to flow, therefore the diode works as a rectifier for AC). The absence of these electrons attracted by the anode will now lead to a higher amount of electrons leaving the cathode to maintain the space charge equilibrium. This will work as long as we apply enough heating power for at least as many electrons to overcome the work function as will be attracted by the anode. Clearly the voltage applied to the anode will influence the amount of electrons attracted, so the higher this voltage the more electrons must be released by from the cathode to maintain the equilibrium. This is the usual mode of operation for vacuum tubes and for obvious reasons called space charge limited operation.

Basically the connection between (anode) voltage and current is given by the formula:

with

• K … constant depending on tube geometry
• V_a … anode voltage

So generally anode current ist proportional to \(V_{a}^{3/2}\), this 3/2-power law is fundamental for all vacuum tubes as long as they are operated under the space charge regime. The Langmuir-Child law exactly specifies current density as a function of anode voltage.

with

• d … distance between cathode and anode

At some point further increasing the anode voltage leads to the situation that the cathode can no longer supply enough electrons leading the space charge to slowly disappear. The current between the anode and the cathode now is no longer proportional to the voltage applied - the tube is now operating in saturation. Note that of course the 3/2-power law is no longer valid in the saturation region.

This leads to the second important law describing the relation between cathode material, heater power and current (density), the Richardson-Duchman equation.

with

• A … material constant (theoretically \({120A} / {\frac {cm^2}{°K}} \))
• T … cathode temperature
• k … Boltzman’s constant
• W … work function of the respective cathode material

Conclusions

The above two formulas show the main influences on the current through a vacuum diode. With a given cathode material (i.e. constant work function), in standard (space charge limited) operation the cathode temperature will be held constant and current therefore obeys the 3/2-power law. On the other hand the Richardson-Duchman formula clearly points out that we can change the (maximum) current by altering the cathode temperature (i.e. changing the heater power).

The diagram below (based on the saturation curve from Sylvania’s 5722 noise diode) gives an impression on the I_a (“plate current”) to V_a (“plate voltage”) relations with different heater power (expressed as filament voltage i.e. heater voltage E_F).

[Fig. 1: Saturation curves of 5722 noise diode]

The next post in this series will uncover how to use the facts acquired in this (and the preceding) article(s) for the proper operation of a noise diode.

¹) As a matter of fact the effect had been reported before by Becquerel (1858) and Guthrie (1873). Most probably the fact that the electron as the main negative charge carrier was only discovered by Thomson in 1893 prevented that scientists drew the right conclusions from these observations any earlier.

²) Only three years later de Forest patented the vacuum triode (the “Audion”), the first amplifying electronic device, although it was Austrian Engineer Robert von Lieben who solved the problem of proportional (i.e. linear) amplification by insertion of a control grid (in it’s narrowest sense) in the electron flow in 1910, after studying de Forest’s patent.

³) From ancient Greek: ἄνοδος -upward and κάθοδος - downward, therefore defining the technical current direction from higher to lower potential, opposite to the physical (electron flow) direction.

References