Page:Alan Turing - Proposed Electronic Calculator (1945).pdf/44

 15. The Design of Valve-elements.

(i) Outline of the problem.- To design valve-elements with properties as described in § 5 and to work at a frequency of say 30 or 100 kilocycles would be very straightforward. When the pulse recurrence frequency is as high as a megacycle we shall have to be more careful about the design, but we need not fear any real difficulties of principle about working at these frequencies, and with such band widths. The successful working of television equipment gives us every encouragement in this respect. A word of warning might perhaps be in order at this point. One is tempted to try and carry the argument further and try to infer something from the success of R.D.F. at frequencies of several thousands of megacycles. Such an analogy would however not be in order for although these very high frequencies are used the bandwidth of intelligence which can be transmitted is still comparatively small, and it is not easy to see how the band width could be greatly increased.

In this chapter I shall discuss the limitations inherent in the problem, and shall also show very tentative circuit diagrams by way of illustration. These circuits have not yet been tried out, and I have too much experience of electronic circuits to believe that they will work well just as they stand. (This does not represent a superstitious belief in the cussedness of circuits and the inapplicability of mathematics thereto. Rather it means that normally the amount of mathematical argument required to get a reliable prophecy of the behaviour of a circuit is out of proportion to the small trouble required to try it out, at any rate if one is in an electrical laboratory. In practice one compromises with a rough mathematical argument and then follows up with experiment. The apparent ‘cussedness’ of electronic circuits is due to the fact that it is necessary to make rather a lot of simplifying assumptions in these arguments, and that one is very liable to make the wrong ones, by false analogy with other circuits one has dealt with on previous occasions. The cussedness lies more in the minds dealing with the problem than in the electronic circuits themselves.)

(ii) Sources of delay.- There are two main reasons why vacuum tubes should cause delays, viz. the input capacity and the transit time. Of these perhaps the first is in practice the more serious, the second the more theoretically unavoidable.

The delay due to the input capacity, when the valves are driven to saturation or some other limiting arrangement is used, is of the order of C/gm, where C is the input capacity and gm is the mutual conductance of the valve. We may, for instance consider the idealised circuit Fig. 44. (Coupling with a battery is of course not practical politics, but it produces essentially the same effects as more practical circuits, and is more easily understood). If I is the saturation current then the grid swing required to produce it is I/gm and the charge which must flow into the grid to produce this voltage is CI/gm. If the whole saturation current is available the time required is C/gm. This argument is only approximate, and omits some small purely numerical factors. However it illustrates the more important points. In particular we can see that Miller effect is not a very serious matter because of the limiting, which reduces the effective amplification factor to 1. On the other hand, if one valve is used to serve several inputs the delay will be correspondingly increased because the capacity has become multiplied by the number of grids served.

This connecting of several grids to one anode, and a number of other practical points will tend to make the actual delay due to input capacity several times greater than C/gm, e.g. 10 C/gm. The/