The Equilibrium Process

Alec Reeves realised that one of the main drawbacks of PCM was the complexity of coders and the requirement for expensive, fast electronic components. Therefore he devoloped the idea of the equilibrium process. This is to have a system that produces the required result because when that result is achieved, it is in a mimimum energy or equilibrium state.

The main principles of the equilibriumn process are
The Principle of Decisive Action
Reeves wrote: I saw first a general principle: that energy was frittered away by indecisiveness. I saw it in the heating of a switch that has a bad contact - in the better power efficiency of Class C radio transmitters - in the act of human decision making. I saw that as far as possible the switch, the valve, the brain signal to the motor nerves should be either definitely "on" or "off". I labelled this principle: I called it The Principle of Decisive Action. It led at once to the work of me and my team on PTM, Pulse Time Modulation.
The Principle of Cooperation.
In my private, childish language, it is "letting the apparatus do what it naturally wants to do". In more scientific terms, it means that when we use an analogue-to-digital converter we must arrange things so that we store energy internally during the process, directly, in the simplest possible way, in such a manner that when the coding is complete this stored energy, then potential not kinetic, is a minimum. This gives us a feedback coder but of a direct and simple form, the feed back loops involving merely connecting wires with nothing added. You'll see, too, that it involves a "feed forward" feature as well, for what happens at the beginning of the coding process can influence the later parts of it. I saw this most simple, elementary concept first in various mechanical shapes.


An early mechanical model of a 4 digit equilibrium encoder.

If you want to level the sand in a beaker, you can move each grain with tweezers and get it level. Or you can shake the beaker.

Reeves wrote: Consider what a human operator does when he uses a chemical balance. Assume he cannot see the sample to be weighed, and that his box of weights contains binary values. He starts with the largest weight in his box. He notes which way the pointer starts to move.

If he sees that he has not put in enough weight, but that the balance pointer moves very slowly, unless he is a lunatic he doesn't then add his next largest weight, but tries adding one that is several binary steps smaller. He observes and uses two parameters, not just one, so saving unnecessary steps in his weighing process - unlike usual sequential coders, but like the equilibrium variety.


It is this latter method that he propoposed could be used to code and decode signals for transmission digitally and also be used for computation. The use in computation was never attributed to him, but it could be what we now know as neural networks.

He developed coders by the use of mechanical models and empirically built circuit boards. He left it to others to work out a rigourous mathematical description of the process he conceived and demonstrated. An example can be found in the book Principles of Pulse Code Modulation by Kenneth W. Cattermole Click here to get a copy - only available second hand now. But you will find reviews here or indeed could write your own.

At a meeting held at STL on 27 January, 1966 it was decided to abandon Equilibrium Coding

The following is from the minutes:

Mr. Reeves reported that the planned 128 level linear equilibrium coder programme had been completed satisfactorily, and it had been shown that tolerances could be obtained which were as good as other designs of coders.

Advantages of equilibrium coding are
a) less components than other designs - this advantage is now negligible, and
b) the coder is capable of higher speeds than other designs whilst using similar components. Work on the high speed possibilities is being pursued with an analogue model, so that a report may be written, and a lecture given to the I.E.E. on April 15th.

However, as the advantages in 24 channel operation are marginal, and the future market for high speed coders appears small, it was proposed by Mr. Reeves to close the project down, as from now for the 24 channel version, and the high speed version in mid April.

This was agreed upon by all present.

With these words, the equilibrium process and its principles was despatched to the dustbin of history. However there is no doubt that it is something quite strange and unusual and it may well get re-discovered again for some specific purpose or for use with some completely different technology.

Abstract of the Lecture delivered by Mr. A. H. Reeves at the meeting of the Joint Professional Group J.4 held at the Institution of Electrical Engineers on Friday 15th April, 1966, at 5.30 p.m.

The talk will be a glimpse into the future, where coding speed requirements may be well in excess of present normal demands. The subject is a rather new type of analogue-to-digital. convertor believed to have good possibilities at speeds of 1000 megabits per second or higher, in real time. It has feedback combined with feed forward, and needs to use only 2-terminal high-speed devices. As serious study of the high-speed modes started only in 1966, and the analysis of the nonlinear network is not yet complete, the explanations will be mainly qualitative, with only salient quantitative theory. No detailed circuit embodiments will be discussed, only possible principles.

A mechanical model will illustrate the low-speed modes in which the operation approaches normal logic. It will then illustrate the possibility of using delayed coding decisions, with accelerated decision-device rise times without external high-speed, high-gain feedback loops, to increase the speeds about five times. This will be followed by a demonstration of stabilised trigger thresholds by inertia loading.

"Stored negative feedback", a powerful method for stabilising digit weights, and giving further correction to the trigger thresholds will be discussed, using pilot-signal or stochastic inputs. Finally, high-speed sampling-gate problems will be discussed, with new solutions.

A fair knowledge of the theory and practice of modern coding will be assumed.

Please click here for the whole lecture. At the moment there are no figures, I hope to be able to put these up later.

Please click here for an ongoing attempt at an Active-x implementation of the equilibrium coder.