Tubes 201 - How Vacuum Tubes Really Work

Copyright © 2025, John Harper

A long time ago I wrote an article on my web page going beyond the basics of vacuum tube (valve) operation, to explain many things which don't seem to make sense if you only look at those basics. It was essentially a summary of the best textbooks and papers from the era when vacuum tubes were high-tech.

The article is still available there, but I've moved it to my blog to make it more accessible and likely to be found.

Table of Contents

1. Introduction
Emission
Physical Construction
Space Charge and Current Flow
The Triode Field and Operation
Initial Electron Velocity
Noise
Other Things
Multi-Grid Tubes

1. Introduction - the Basics

Everyone knows how a tube works. Current passing through the filament heats it up so that it gives off electrons. These, being negatively charged, are attracted to the positive plate. A grid of wires between the filament (or cathode) and the plate is negative, which repels the electrons and hence controls the current to the plate. For many purposes thats all you really need to know. This article looks beyond the basics, into what makes a tube behave the way it does.

As a start, let's recap the well-known properties of tubes, which will probably be familiar to most people reading this article. We will focus on the use of tubes for audio and will look mainly at triodes, with a look later at multi-grid tubes for audio.

Reassurance for the Math Averse

There are lots of equations in this article. Be assured, if you don't like math, you can skip them. The text tells you the important things that the equations mean. Of course, if you're happy with math, you'll get more from this article. (And there isn't any real math, i.e derivations of things).

The behavior of a triode is fully described by its plate curves, as shown in Figure 1. These show the plate current as a function of plate voltage (on the horizontal axis) and the grid voltage, becoming more negative as we move to the right of the family of curves. The curves for audio tubes generally only show negative grid voltage and positive plate voltage, although it is common to operate transmitting tubes with positive grids, and it is even possible (though rarely useful) to operate with a negative plate. These curves are just a way to represent a three-dimensional surface on the printed page, and in the old days people would even build models from plaster to represent this (e.g. in [Chaff33]). Nowadays we can just ask the computer to draw it for us, as shown in Figure 2. Mathematically, this is a representation of a function which takes two arguments (grid voltage and plate voltage) and gives the plate current as its result. The standard texts (e.g. [Lang53] show how to use these curves to establish the operating conditions for a tube.

Figure 1: Plate Curves for Typical Triode (ECC82/12AX7)

Figure 2: Surface Representation of Triode Curves

There are other ways to represent the same function. For example, we can draw the transfer characteristics, which show plate current as a function of grid voltage, with different curves in the family for different plate voltages. It is also possible to draw curves which show derivatives, such as the values of plate resistance and mutual conductance under different conditions. However these are not different characteristics, just different ways of looking at the same data.

One thing that leaps out is that the plate curves are just that - curves. In fact an ideal amplifying device, at least for audio, would show parallel, equally-spaced straight lines rather than curves. Unfortunately no real-world amplifying device can do this, since they all depend on physical phenomena that result in more complex transfer functions. Incidentally the obsession with linearity is somewhat peculiar to the world of audio. In other branches of electronics, such as RF and video, linearity is not so dramatically important since reasonable non-linearity can be filtered out either electronically (e.g. by tuned circuits) or by the receiving device (e.g. the eye). Only the ear can detect such tiny traces of non-linearity.

The plate curves follow quite closely a ³⁄₂ power law, in which the current increases as a function of the ³⁄₂ power of either the grid or the plate voltage. This is especially true at high currents and in the lower (closer to zero) range of grid voltage. While this is not linear, it is closer to linearity than any solid-state amplifying device, which is the main reason why tube amplifiers are nowadays often considered (and certainly by most of you who will be reading this) to be sonically superior. At low currents, especially as the grid becomes more negative, the ³⁄₂ power law no longer applies and the plate curves tuck under very noticeably. The curves are not equally-spaced, even at high currents, but rather get closer together as current increases. All of this is causes extra non-linearity and distortion. This is more true for some tubes than for others, and later on we will look at some of the reasons.

In the sections which follow we take a look at the reality of tube design, construction and operation, which will explain why tubes behave the way they do. On the way we will explode a few popular myths.

Next: Emission ➡ 

Further Reading and References

Of the many books which were written from 1920 into the 1950s about the theory of vacuum tubes, the two which are by a long way the most comprehensive are Spangenburg [Spang48] and Beck [Beck53]. Unfortunately these are extremely difficult to get hold of. These can really be regarded respectively as the US and UK bible on the subject. Spangenburg does however have a number of baffling minor errors in the transcription of formulae from other sources, which means that reference to original sources is required for certainty.

Dow [Dow37] seems to be easier to find, and gives many of the basic principles as well as a good introduction to the use of tubes in circuits. There is also a later book by Spangenburg [Spang57], although shorter than the first and covering semiconductors as well as tubes, which is quite adequate and seems easier to find.

Reich [Reich41] is fairly basic but has the advantage of being available in a reprint [Reich95]. Valley & Wallman [Valley46] deals largely with DC and pulse amplifiers using tubes, and covers several topics such as low-level amplifiers in more detail than elsewhere.

Mitchell [Mitch93] gives the most comprehensive tube data available, unfortunately only for a small selection of tube types. Smullin [Smullin59] gives a comprehensive treatment of all aspects of noise in vacuum tubes.

[Barb97]	Barbour E.	EL84: The Baby With Bite, Vacuum Tube Valley issue 8, 1997
[Beck53]	Beck A.H.W.	Thermionic Valves, Cambridge University Press, 1953
[Bench99]	Bench S.	Directly Heated Triodes operated with lower voltage on the filaments, available at http://members.aol.com/sbench102/dht.html
[Chaff33]	Chaffee E.L.	Theory of Thermionic Vacuum Tubes, McGraw-Hill, 1933
[Dow37]	Dow W.G.	Fundamentals of Engineering Electronics, Wiley, 1937
[Frem39]	Fremlin J.H.	Calculation of Triode Constants, Electrical Communications, July 1939
[Lang23]	Langmuir I.	The Effect of Space Charge and Initial Velocities on the Potential Distribution and Thermionic Current Between Parallel Plane Electrodes, Physics Review vol. 21 pp419-435, 1923
[Lang53]	Langford-Smith F.	Radiotron Designers Handbook, Iliffe, 1953
[Max71	Maxwell J.C.	A Treatise on Electricity and Magnetism, 1871, reprinted by Dover Publications, 1954, ISBN 0-486-60636-8
[Mitch93]	Mitchell T.	The Audio Designers Tube Register, Media Concepts, 1993, ISBN 0-9628170-1-5
[Reich41]	Reich H.J.	Principles of Electron Tubes, Wiley, 1941
[Reich95]	Reich H.J.	Principles of Electron Tubes, reprinted by Audio Amateur Press, 1995, ISBN 1-882580-07-9
[Smullin59]	Smullin L.D. & Haus H.A.	Noise in Electron Devices, MIT Press, 1959
[Spang48]	Spangenburg K.R.	Vacuum Tubes, McGraw-Hill, 1948
[Spang57]	Spangenburg K.R.	Fundamentals of Electron Devices, McGraw-Hill, 1957
[Valley46]	Valley G.E. & Wallman H.	Vacuum Tube Amplifiers, MIT Press, 1946, reprinted by Boston Technical Publishers Inc., 1964 Revision 2, 2 January 2002.